As the name indicates, a "supporting" detail is there to give more support to your argument. A supporting detail is one that strengthens your position by providing examples, facts or details that bring evidence to your statements. Therefore, supporting details are essential elements in any text, as they allow you to develop your ideas, and create a more persuasive text.
Elimination is always the best. Pick out the worst possible answers, so it'll give you less choices to pick from. Or you could always pick c. I wouldn't advise that. Good luck on your test. :)