We need to evaluate the expression $(-2)^3 \div (-3)^3 \times (-6)^2 \div 4^2$.

1. Problem Description

We need to evaluate the expression $(-2)^3 \div (-3)^3 \times (-6)^2 \div 4^2$.

2. Solution Steps

First, we evaluate the powers:

$(-2)^3 = -8$

$(-3)^3 = -27$

$(-6)^2 = 36$

$4^2 = 16$

Now we substitute these values into the expression:

$-8 \div (-27) \times 36 \div 16$

We can rewrite division as multiplication by the reciprocal:

$-8 \times \frac{1}{-27} \times 36 \times \frac{1}{16}$

Rearrange to make it easier to compute:

$\frac{-8}{-27} \times \frac{36}{16}$

Simplify each fraction:

$\frac{8}{27} \times \frac{9 \times 4}{4 \times 4}$

$\frac{8}{27} \times \frac{9}{4}$

Simplify further:

$\frac{2 \times 4}{3 \times 9} \times \frac{9}{4}$

$\frac{2}{3} \times \frac{4}{4} \times \frac{9}{9}$

$\frac{2}{3} \times 1 \times 1$

$\frac{2}{3}$

3. Final Answer

2/3