How does Jack’s mask allow him to behave differently in chapter four of "Lord of the Flies?"
This is actually a pretty common phenomenon, at least among some people. The act of putting on a mask seems to allow some people to behave in ways they otherwise wouldn't be able to. On the one hand, you can think of all the serial killers in the movies (Jason, Michael Myers, Leatherface) and on the other hand you can think of the jerk at the football game who paints his face, wears a beer hat, and screams a lot.
Jack's "mask" is really some improvised makeup, but it works in the same sort of fashion. As soon as he gets it the way he wants it, kind of creepy like, he is thrilled:
He looked in astonishment, no longer at himself but at an awesome stranger. He spilt the water and leapt to his feet, laughing excitedly.
The mask has allowed him to become something different, an "awesome stranger."
He began to dance and his laughter became a bloodthirsty snarling. He capered toward Bill, and the mask was a thing on its own, behind which Jack hid, liberated from shame and self-consciousness.
This really hits at the heart of it. Notice the part of the quote where it says "Jack hid, liberated from shame and self-consciousness." The mask, essentially, allows Jack to put aside morality and a lot of the social conventions that might otherwise govern his behavior.
“I cut the pig’s throat,” said Jack, proudly,"
This is the ultimate product of the mask. It has allowed Jack to do what he could not previously stomach: kill the pig.