Construct a 3x3 grid to represent the pairs (x, y) where x = 0, 1, 2 and y = 0, 1, 2.

Pr(X = x, Y = y) = Pr(X = x) Pr(Y = y) since X and Y are independent.

And you should know how to use the binomial distribution to calculate the probabilities of X = x and Y = y for x = 0, 1, 2 and y = 0, 1, 2.