The problem requires us to simplify the expression $-3a^2b(2ab^2 - 2b)$. This involves distributing $-3a^2b$ to both terms inside the parentheses.

1. Problem Description

The problem requires us to simplify the expression $-3a^2b(2ab^2 - 2b)$. This involves distributing $-3a^2b$ to both terms inside the parentheses.

2. Solution Steps

First, distribute $-3a^2b$ to $2ab^2$:

$(-3a^2b) * (2ab^2) = -3 * 2 * a^2 * a * b * b^2 = -6a^{2+1}b^{1+2} = -6a^3b^3$

Second, distribute $-3a^2b$ to $-2b$:

$(-3a^2b) * (-2b) = -3 * -2 * a^2 * b * b = 6a^2b^{1+1} = 6a^2b^2$

Combining the two terms, we get:

$-6a^3b^3 + 6a^2b^2$

3. Final Answer

$-6a^3b^3 + 6a^2b^2$