Try an example. In this particular problem, one example is sufficient because for each expression f(x,y) (i.e., f(x,y) = xy, f(x,y) = xy + 2, etc.), f(x,y) is either always even or always odd under the assumption that x and y are odd.
However, you should also be able to prove the correct answer. Since x is odd, x can be represented as 2x' + 1 for some integer x'. For example, 7 = 2 * 3 + 1 and -7 = 2 * (-4) + 1. Similarly, y = 2y' + 1 for some integer y'. What do you get when you multiply x and y and simplify the result?