First, find a common denominator: $8xy$

Rewrite each expression using 8xy as the denominator: $\frac{-4y}{8xy}-\frac{2x}{8xy}+\frac{8}{8xy}+\frac{xy}{8xy}$

Add up the numerators: $-4y-2x+8+xy$ (since the denominator is the same in all answer choices, we can disregard it)

Group the x terms together and the y terms together: $xy-4y-2x+8$

Factor each group: $y(x-4)-2(x-4)$

And distribute: $(x-4)(y-2)$

Only one answer choice matches that numerator.

Answer: C