Indirect Proof

Disclaimer: I have never taken a course in formal logic. I have, however, written tons of proofs by contradiction. ("Proof by contradiction" = "indirect proof" = "reductio ad absurdum.")

Here's how I would suggest going about it:

Start by assuming the negation of "~ W v ~ M". In other words, start by assuming that "~ (~W v ~M)" is true. By De Morgan's laws and the law of double negation, that last statement is equivalent to "W ^ M". From there, use the two premises to derive the contradiction "M ^ ~M". That's a sketch of how your indirect proof should work.