What is the value of X when your angle is 45 degrees and your opposite hypotenuse is 8 and your adjacent is unknown.?

　
Your question is confusing. The opposite side to the 45 degree angle is not the hypotenuse. So I'm not sure what side you are referring to.

Assuming this is a right triangle, then we have 2 cases in this ambiguous question:

Opposite side is 8.
In that case, adjacent is also 8.

Hypotenuse is 8.
In that case opposite = adjacent = x
x² + x² = 8²
2x² = 64
x² = 32
x = 4√2

tan(theta) = opposite/adjacent
tan(45°) = 8/adjacent
1 = 8/adjacent
adjacent = 8
The answer is C.

Diagram ?