To solve this equation, we first need to simplify both sides by using the properties of logarithms.

Starting with the left side of the equation:

2log4(4-x) = log4((4-x)^2)
2log4(4-x) = log4((16-8x+x^2))
2log4(4-x) = log4(x^2 - 8x + 16)

Now, moving to the right side of the equation:

4-log2(-2-x) = log2((-2-x)^4)
4-log2(-2-x) = log2((-2-x)^4)
4-log2(-2-x) = log2((-2-x)^4)
4-log2(-2-x) = log2((-16 - 8x + x^2))

Now we have simplified the equation to:

log4(x^2 - 8x + 16) = log2(x^2 - 8x - 16)

To solve for x, we set the expressions inside the logarithms equal to each other:

x^2 - 8x + 16 = x^2 - 8x - 16

Subtracting x^2 and adding 8x from both sides, we get:

32 = -32

This is a contradiction, so there are no solutions to this equation.