Consider the values taken by X and the values taken by Y.
Then find the possible values for XY, by multiplying the possibilities.
Then find the probability to get a given value for XY.
for example, if X can have value a with probability p, and Y can have value b with probability q, then P(XY=ab)=P(X=a,Y=b)
And if X and Y are independent, then P(X=a,Y=b)=P(X=a)P(Y=b)