Use De Morgan's law on the right-hand side, then apply distributivity to the result, i.e., transform it into a disjunction of conjunctions. Simplify, and you'll get the left-hand side.
I have tried doing this:
(P ^ ¬Q) V (¬P ^ Q) <=> ¬(P ^ Q) ^ (P VQ)
Swap sides
¬(P ^ Q) ^ (P VQ) <=> (P ^ ¬Q) V (¬P ^ Q)
Hence, since ¬(P ^Q) <=> ¬P V ¬Q (using De Morgan's Laws)
This gives us:(¬P V ¬Q) ^ (P V Q)
And in turn, (¬P V ¬Q) ^ (P V Q)<=> (P ^ ¬Q) V (¬P ^ Q)
However, I can't seem to figure out where to go from here.