So I've been pretty much staring at this all night and I honestly have no clue as to what to do. I have attached the problem, so if someone could help out or just point me in the right direction, it would be greatly appreciated.

 

Do you have any knowledge on building logic functions with MUXes?

If so, did you notice that the function you want to build is comprised by a sum of terms that consist of an expression multiplied by all the permutations of A and B?

In general, when you see an expression of the type X*A+X'*B, that can be build by giving X at the MUX's select and A and B in their respective inputs. In the same logic, for an expression X'Y'*A+X'Y*B+XY'*C+XY*D, X and Y are the select variables and A,B,C,D are the inputs.

Can you use that to build the function given?

I admit that I simplified a little C and D epxressions in brackets in order to get rid of the small MUXes. I built the whole function using only the big MUX.

It was an interesting exercise all in all.