Out of all the pronouns, "whom" makes the most sense grammatically. This allows us to narrow it down to A or D.
In order for it to be the object of a preposition, there would have to be a preposition in front of it. "For," however is <em>not</em> a preposition. In fact, there isn't a preposition in the whole question.
This leaves us with option D, which is the correct answer.
You can better tell it's a direct object if you flip the sentence around a bit. Your sister is waiting <em>for whom</em>? "Whom" is essentially receiving the action. "Whom" is what your sister is waiting for.
