I guess question is "at least two cards each of two different kinds".
We can only have 13 cards of one kind. So, in the worst case we pick these 13 cards all of same kind. Now, if we pick the next card of a different kind, we can do like this only 3 more times- as there are only 4 different kinds. The fourth time we do, we must repeat a kind. So, 13+4 = 17 is the answer.