Somewhat trivial, but here goes: in Fullmetal Alchemist, we see Mustang's hands get pinned down by Bradley's swords when Wrath and Pride are trying to force him to do human transmutation and open the gate. Given this, how does he manage to participate in the fight against Father later (probably in chapter 107 or a slightly earlier chapter) given that his "attack" requires use of his hands (and that he doesn't seem to start using circleless transmutation until he has to fend off a counterattack)?
This is just a scenario of the shounen genre doing whatever it feels like. Biologically, he would have taken serious damage to bones, nerves, muscles, etc. when his hands were stabbed through. But in anime, particularly in the shounen genre, characters can often overcome this type of thing with relative ease.
Take, for example, a scene from Shingeki no Kyojin (Attack on Titan) wherein one of the characters literally has a plank stabbed through a lung, and still manages to somehow sit up—dragging the plank through their body—while spurting blood everywhere.
In Mustang's case, there is no evidence that he was healed in any fashion (such as by May Chang), nor that he is impervious to hand pain in any way. He is simply able to do this because the mangaka decided it was necessary to the story. That's the power of shounen!
This may not make any sense or be true, but assuming that immediately following Wrath removing the swords from Mustang's hands he was forced by Pride to transmute, it is possible that during the deconstruction and reconstruction, the injuries were at least sealed up, or possibly healed altogether, seeing as he was alchemically torn apart and pieced back together.
I get your question. Irl, there's no way. There are just too many bones, ligaments and tendons in the hand (not to mention the tremendous amount of pain an injury like that would incur) to be able to do that. BUT, FMAB is fiction, so OF COURSE HE CAN. FWIW, the FMA fandom wiki says this about the actual sound of snapping when Roy does his thing: The 'snap' sound heard at the start of these transmutations is caused by the instantaneous speed at which the highly concentrated gases and sparks react together and pop (and not Mustang's fingers actually 'snapping', to common belief.) I don't think it could be done irl, but ymmv.