The answer that is INCORRECT is (c). You can think of instances where (a), (b), and (d) would be correct, but (c) makes absolutely no sense: "I told her that she mightiest have gone there."
Although I agree with your conclusion that (a), (b), and (c) are all possible, I would like to correct your analysis:
(d) I told her that she shouldn't have gone there. This implies an after-the-fact discussion. I told her (after she already went) that she shouldn't have gone. If you told her not to go, and she went anyway, then you would say, "I told her she shouldn't go."
(a) I told her that she mustn't have gone there. This one is a little trickier. The way it reads, it sounds like she (the one who went there), or someone else, believes that she went there, but there is other strong evidence to say otherwise. For instance, let's say she is suspected of a crime, and to police says she was at the scene. However, surveillance photos from a bank put here somewhere else when the crime was committed. Then her lawyer would tell her, "You must not have gone there." (And then told someone else that "I told her that she mustn't have gone there."
(b) I told her that she will have gone there. I agree with what you said about (b) except it's a prediction that she will have been there, not just left for there.
Sorry for being so wordy, but I hope it helps.