Misogyny is the hatred or discrimination against women, so your answer should be two words that have that relationship. You know that A is not correct because divest means to take away possessions, and that isn't hatred against property. You know that B is not correct because pathological means relating to disease, not hatred to disease. Finally, you know that C can't be the right answer because progeny means descendants, not hatred of children.
Misogamy is the hatred of marriage, so D is your answer.
Well an expository essay is a writing peice that explains your topic or whatever you plan to write about and when you write you can really use any method but it has to sound right and feel right.