Here is the problem:
9a^3 + 6a^2 4b^3 − 10ab^3
-------------- * ------------------- =
10ab − 4b 9a^2 + 6a

Here is what I got:
3x^2 (3x+2) 2b^3(2-5a)
---------------- * ---------------
2b (5a-2) 3a(3a+2)

Now what?

I will assume you meant 3a^2(3a + 2), since there are no x terms in the equation.
What you have to do is change the (2-5a) to equal (5a-2).
Multiply what is outside of that bracket by -1, so you get:
2b^3(2-5a)
= -2b^3(5a-2)
Now cancel out everything in brackets so you are left with:
(3a^2 * 2b^3) / (2b * 3a)
(6 * a^2 * b^3) / (6 * a * b)
Since a = a^1, use the laws of dividing exponents which say that a^5 / a^3 = a^(5-3) = a^2
a^2 / a^1
= a^(2-1)
= a^1
= a
b^3 / b^1
= b^(3-1)
= b^2
So you are left with:
(1 * a * b^2) / (1)
= ab^2