Let's do process of elimination. The first choice is incorrect since it uses "who" instead of "whom." That's just proper grammar. The last choice is also incorrect because it says "him and me" when it should say "him and I." Once again, that's just proper grammar. The third choice is also incorrect because it says "he and I" which again, is grammatically incorrect. Therefore, your answer is the second choice. As to how you do this yourself, I would suggest reading all of the choices and see which one sounds correct. Hope this helps.
