The best procedure is usually to work from the inside out. So, for instance, your first step would be something along the lines of:
. . . . .-5x - 2[4x - 2(3y - 8) - (3x + 2y)]
. . . . .-5x - 2[4x - 2(3y - 8) - 1(3x + 2y)]
. . . . .-5x - 2[4x - 2(3y) - 2(-8)) - 1(3x) - 1(+2y)]
Simplify, and combine like terms. Then take the -2 through the brackets. And so forth.
If you get stuck, please reply showing how far you have gotten. Thank you.
Eliz.