Simplify the numerator and divide.?

[-8a^3q - 16a(aq^2 - a^2q)]/[20a^2q^2]
= [-8a^3q - 16a^2q^2 + 16a^3q]/[20a^2q^2]
= [-8a^3q + 16a^3q - 16a^2q^2]/[20a^2q^2]
= 8a^2q[a - 2q]/[20a^2q^2]
= [8a^2q/20a^2q^2][a - 2q]
= [2/5q][a - 2q]
= 2[a - 2q]/5q
= 2/5 * [a - 2q]/q
= 2/5 * [a/q - 2q/q]
= [2/5][a/q - 2]

Numerator, N= -8a^3q -16a(aq^2 -a^2q):
Separating out common factors and putting the rest in brackets
- 4a^2q{ 2a + 4(q - a)}
Now
- 4a^2q{ 2a + 4(q - a)}
__________________ =
4a^2q(5q)
[cancel out identical quantities in Num & Denom]
- 2[a + 2(q - a)]
_____________ = (N/D)
5q

You forgot laws of indices Panther, haven't you?
Nr = - 8(a^3)q - 16(a^2)(q^2) + 16(a^3)q
= 8(a^3)q - 16(a^2)(q^2)
= 8(a^2)q [ 1 - 2q]
so fraction = 2(1-2q)/5qa^3
I assumed a^3 q to be (a^3)q NOT a^(3q)

-8a^3q - 16a(aq^2 - a^2q)
----------------------------------- =
20a^2q^2

-8a^3q - 16a^2q^2 + 16a^3q
----------------------------------------- =
20a^2q^2

8a^3q - 16a^2q^2
----------------------------- =
20a^2q^2

8a^3q - 16a^2q^2
---------- --------------- =
20a^2q^2 20a^2q^2

2a 4
------- - ------- =
5q 5

25q( 2a/5q - 4/5) = 10aq - 20q =

10q(a-2q)

= -8a^3 q - 16a^2q^2 + 16a^3q / 20a^2 q^2 (multiply out the bracket)

= 8a^3q - 16 a^2 q^2 / 20a^2 q^2 (simplify)

= 4 a^2q (2a - 4q) / 4a^2 q (5q) (find a common factor on top and bottom)

= 2a- 4q / 5q OR 2(a-2q) / 5q (divide top & bottom by 4 a^2q)

First: distribute the top:

You get (-8a^3q - 16a^2q^2 + 16a^3q).
Combine like terms and you have 8a^3q - 16a^2q^2.

Factor out 8a^2q.

8a^2q(a-2q)/(20a^2q^2)

Reduce: 2(a-2q)/5q