To solve this equation, we can simplify both sides first.

Starting with the left side of the equation:
(-2)^x = (-2)^x

Now let's simplify the right side of the equation:
(-8)^4 / (-32)^3

(-8)^4 = (-8)(-8)(-8)(-8) = 4096
(-32)^3 = (-32)(-32)(-32) = -32768

Therefore, the equation becomes:
(-2)^x = 4096 / -32768

Simplifying further:
(-2)^x = -1/8

Now, we need to find the value of x that satisfies this equation. Taking the logarithm of both sides can help us solve for x:

log[base -2](-2)^x = log[base -2](-1/8)

x = log[base -2](-1/8)

However, logarithms with negative bases are not defined in the real number system. Therefore, there is no real solution for x in this equation.