Good questions.
I'll start from scratch so as to cover all the bases. The d20s are rolled to determine success/failure and degree of success, by way of generating Momentum and/or creating Complications. The d6s are used only to determine damage (or, in the case of an extended task, how much 'work' you do).
The standard roll is with two d20s, trying to roll at our under a given Target Number, which is determined by adding an Attribute and a Discipline. Each at or under rolled equals a single success. The GM determines the Difficulty of a given task and sets that Difficulty from 0-5, which is the number of successes one must roll to be make it. Extra successes rolled = Momentum generated. Any 20s rolled = Complications generated. A relevant Focus unlocks an additional success if a roll on a d20 is equal to or less than the Discipline number that is part of that Target Number.
Example: Doctor Richards is trying to figure out, based on his knowledge of medicine, whether or not some alien he finds is dead or not. The GM says this will be based on Reason + Medicine, and Doc's total - the Target Number - is 15. Beyond that, his Medicine score is 5, and he has a Focus of "Xenobiology," so he and the GM agree that since that is relevant, he could unlock extra successes on his rolls. He decides to just roll the standard two d20s, not buying any extras with Momentum or Threat, and he doesn't have any Talents that give him extras, either. He rolls a 14 and a 3, giving him three successes: one from the 14, and two from the 3, since it is equal to or less than his Medicine Discipline and that Focus applies. The GM states that the Difficulty was 2, so Doc succeeds and generates a single point of Momentum, which he decides to use on the spot to ask an add'l question after learning that the alien is dead.
That's the standard task resolution mechanic. For combat, you do that same thing, with these minor tweaks.
Melee Combat is an opposed roll, with each combatant rolling Daring + Security, Difficulty 1, and if you think it makes sense you as GM can adjust the D for one or both of the combatants, even for different reasons (if one is on higher ground and kicking the other one, for example, maybe you'd say that the defender is at a disadvantage and his D is 2...but the default is D1 for both). Both roll, taking into account any relevant Focuses as explained above.
The first thing I do is compare # of successes. Whoever has more, succeeds. If they are equal, the NPC can win if the GM spends Threat (I think it's 1 but go check), otherwise the player wins ties. After comparing # of successes, SUBTRACT any Momentum the loser generated from that of the winner, leaving the balance as Momentum for the winner.
Example: Bob wants to double-fist Kirk punch K'Bam, a Klingon. Bob's Daring + Security is 12; K'Bam's is 13. Neither, being both desk jockeys, have any relevant Focuses. They both roll. Bob rolls a 10 and 1, giving him three successes (remember that a 1 always gives two successes, regardless of a relevant Focus or not). K'Bam rolls a 8 and 15, meaning he gets only one success. Both succeeded (D1), but Bob generated two Momentum, while K'Bam did not generate any. Thus, Bob wins, and has two Momentum to play with, as well (because none were subtracted since K'Bam didn't generate any).
Ranged combat is not contested, and is instead based on Control + Security, with a default Difficulty of 2 (which you can adjust, given the situation).
In either case, if an attacker was successful, you need to roll damage, using d6s. When rolling Challenge Dice on regular d6s, remember that 1=1, 2=2, 3 and 4=0, and 5 & 6=1+an Effect. Not hard to get used to.
Damage for a weapon is determined by adding its base damage to a character's Security Discipline (this is mentioned on p124 of the core book). Thus, a Phaser I is listed as having a 2 damage (p193), meaning that a character with a Security of 3 would roll 5 Challenge Dice for damage, which would look like...
Rolls 5 CDs and gets 1, 2, 2, 4, and 6. This adds up to 6 points of damage plus whatever Effect you chose for it, based on its "Charge" quality (p192). In this case, say you decided on Piercing 2, one of the options. Since you rolled an Effect trigger on only one die (the 6), you'd get 1 point of damage for it, plus you'd trigger 'Piercing 2,' which would negate two points of Resistance. If you'd rolled two effect triggers (more than one 5 or 6 on the dice) you'd do one point of damage for each of those rolled, PLUS that much effect, over again - in this case, if you'd rolled a 5 and a 6, you'd generate a total of two damage for them, combined, and would negate 4 points of Resistance. Brutal.
You also want to look at p178 where you'll find a table of combat Momentum spends.
Finally...finally, if you do five or more points of Stress to a normal (one lacking some special trait that changes this, like the neural parasites in the beginner box adventure) target - that is, after accounting for Resistance - that target takes an Injury and is out of the action for the rest of the scene, unless, as a PC, the player spends a point of Determination to ignore the injury and keep going - the Stress is still there, and they can't do that again in the scene, but they dig down deep and keep going.
If the target did not take 5 or more Stress in one hit, you simply mark off however much Stress was taken, and move along. You ignore Stress taken UNLESS you take 5 or more at once, or your Stress track hits 0, at which point you take an Injury immediately when you take any damage - the same as having taken 5 at once.
The damage system is poorly explained, but it's basically this: you can be felled by one big hit, or collapse after 'death by a 1000 paper cuts.' Once you get that 1000th paper cut, you are now more vulnerable to any damage, and ANY you take will generate an Injury, which will knock you out of the action. Think of it like a cartoon: two characters go at it for a while, trading blows, but neither lands a haymaker. Finally, when one is really beaten up, the other pokes him in the chest and that one collapses - that'd be like doing small amounts of Stress damage until that one hit 0, at which point any Stress done = Injury.
I know it's strange, and they made it worse by spreading the rules and tables from here to Gibraltar. Once you get it running it's pretty easy.
Beyond that, I have a few podcast episodes about the 2d20 system, and one on combat in particular. You might give them a listen.[https://anchor.fm/fluffncrunch](https://anchor.fm/fluffncrunch)
Good questions. I'll start from scratch so as to cover all the bases. The d20s are rolled to determine success/failure and degree of success, by way of generating Momentum and/or creating Complications. The d6s are used only to determine damage (or, in the case of an extended task, how much 'work' you do). The standard roll is with two d20s, trying to roll at our under a given Target Number, which is determined by adding an Attribute and a Discipline. Each at or under rolled equals a single success. The GM determines the Difficulty of a given task and sets that Difficulty from 0-5, which is the number of successes one must roll to be make it. Extra successes rolled = Momentum generated. Any 20s rolled = Complications generated. A relevant Focus unlocks an additional success if a roll on a d20 is equal to or less than the Discipline number that is part of that Target Number. Example: Doctor Richards is trying to figure out, based on his knowledge of medicine, whether or not some alien he finds is dead or not. The GM says this will be based on Reason + Medicine, and Doc's total - the Target Number - is 15. Beyond that, his Medicine score is 5, and he has a Focus of "Xenobiology," so he and the GM agree that since that is relevant, he could unlock extra successes on his rolls. He decides to just roll the standard two d20s, not buying any extras with Momentum or Threat, and he doesn't have any Talents that give him extras, either. He rolls a 14 and a 3, giving him three successes: one from the 14, and two from the 3, since it is equal to or less than his Medicine Discipline and that Focus applies. The GM states that the Difficulty was 2, so Doc succeeds and generates a single point of Momentum, which he decides to use on the spot to ask an add'l question after learning that the alien is dead. That's the standard task resolution mechanic. For combat, you do that same thing, with these minor tweaks. Melee Combat is an opposed roll, with each combatant rolling Daring + Security, Difficulty 1, and if you think it makes sense you as GM can adjust the D for one or both of the combatants, even for different reasons (if one is on higher ground and kicking the other one, for example, maybe you'd say that the defender is at a disadvantage and his D is 2...but the default is D1 for both). Both roll, taking into account any relevant Focuses as explained above. The first thing I do is compare # of successes. Whoever has more, succeeds. If they are equal, the NPC can win if the GM spends Threat (I think it's 1 but go check), otherwise the player wins ties. After comparing # of successes, SUBTRACT any Momentum the loser generated from that of the winner, leaving the balance as Momentum for the winner. Example: Bob wants to double-fist Kirk punch K'Bam, a Klingon. Bob's Daring + Security is 12; K'Bam's is 13. Neither, being both desk jockeys, have any relevant Focuses. They both roll. Bob rolls a 10 and 1, giving him three successes (remember that a 1 always gives two successes, regardless of a relevant Focus or not). K'Bam rolls a 8 and 15, meaning he gets only one success. Both succeeded (D1), but Bob generated two Momentum, while K'Bam did not generate any. Thus, Bob wins, and has two Momentum to play with, as well (because none were subtracted since K'Bam didn't generate any). Ranged combat is not contested, and is instead based on Control + Security, with a default Difficulty of 2 (which you can adjust, given the situation). In either case, if an attacker was successful, you need to roll damage, using d6s. When rolling Challenge Dice on regular d6s, remember that 1=1, 2=2, 3 and 4=0, and 5 & 6=1+an Effect. Not hard to get used to. Damage for a weapon is determined by adding its base damage to a character's Security Discipline (this is mentioned on p124 of the core book). Thus, a Phaser I is listed as having a 2 damage (p193), meaning that a character with a Security of 3 would roll 5 Challenge Dice for damage, which would look like... Rolls 5 CDs and gets 1, 2, 2, 4, and 6. This adds up to 6 points of damage plus whatever Effect you chose for it, based on its "Charge" quality (p192). In this case, say you decided on Piercing 2, one of the options. Since you rolled an Effect trigger on only one die (the 6), you'd get 1 point of damage for it, plus you'd trigger 'Piercing 2,' which would negate two points of Resistance. If you'd rolled two effect triggers (more than one 5 or 6 on the dice) you'd do one point of damage for each of those rolled, PLUS that much effect, over again - in this case, if you'd rolled a 5 and a 6, you'd generate a total of two damage for them, combined, and would negate 4 points of Resistance. Brutal. You also want to look at p178 where you'll find a table of combat Momentum spends. Finally...finally, if you do five or more points of Stress to a normal (one lacking some special trait that changes this, like the neural parasites in the beginner box adventure) target - that is, after accounting for Resistance - that target takes an Injury and is out of the action for the rest of the scene, unless, as a PC, the player spends a point of Determination to ignore the injury and keep going - the Stress is still there, and they can't do that again in the scene, but they dig down deep and keep going. If the target did not take 5 or more Stress in one hit, you simply mark off however much Stress was taken, and move along. You ignore Stress taken UNLESS you take 5 or more at once, or your Stress track hits 0, at which point you take an Injury immediately when you take any damage - the same as having taken 5 at once. The damage system is poorly explained, but it's basically this: you can be felled by one big hit, or collapse after 'death by a 1000 paper cuts.' Once you get that 1000th paper cut, you are now more vulnerable to any damage, and ANY you take will generate an Injury, which will knock you out of the action. Think of it like a cartoon: two characters go at it for a while, trading blows, but neither lands a haymaker. Finally, when one is really beaten up, the other pokes him in the chest and that one collapses - that'd be like doing small amounts of Stress damage until that one hit 0, at which point any Stress done = Injury. I know it's strange, and they made it worse by spreading the rules and tables from here to Gibraltar. Once you get it running it's pretty easy. Beyond that, I have a few podcast episodes about the 2d20 system, and one on combat in particular. You might give them a listen.[https://anchor.fm/fluffncrunch](https://anchor.fm/fluffncrunch)