I'm so confused how do you expand brackets and ?

Expanding brackets is just your book's way of saying to use the distributive property and then simplify to solve each equation.

I'll show the work for a and b and then the answers for the rest.

a. 

4(g + 5) - 4g 

Multiply each part inside the parentheses by 4

4g + 4(5) - 4g
4g + 20 - 4g

Now combine like terms to simplify the equation. In this case, the 4g and - 4g cancel each other out.

4g - 4g + 20
0 + 20
20

20 is your answer.

b.  

6(p + 4) + 2(p - 12)

Multiply each part of the first set of parentheses by 6 and the second set by 2

6p + 6(4) + 2p + 2(- 12)
6p + 24 + 2p - 24

Combine like terms

6p + 2p + 24 - 24
8p + 0
8p

8p is your answer

c. 6z

d. 3a + 8

e. 8a + 16 which simplifies 8(a + 2)

f. 32w + 16 which simplifies 16(2w + 1)