I'm completely confused, please help explain how my teacher got this answer.

How many board feet is the walking surface of my deck? How many boards are installed?

This is the key she gives:
2” x 6” x 16’ long… 24’ / 6” = 24’ / .5’ = 48 boards

Answer: 16 BF/Board x 48 Boards=
768 Board feet required for the walking surface of the deck.

How is she getting this?

Thanks in advance.

Because the boards are 2 inches thick, each square foot of deck area is 2 board feet. You have not told us what the area of the deck is.. only that you are using 16' long boards of 2"x6" cross section. each of this boards is 2*(1/2)*16 = 16 board feet. 48 boards is indeed 768 b.f.

Your deck area must be 48 boards x 8 s.f/board = 384 s.f. It might be 24 x 16 feet, but you don't tell us. They should have specified the deck area somewhere.