Which form of government serves the interests of royal family members?

a democracy

a monarchy

a theocracy

an oligarchy

It can't be a democracy: in a democracy the government serves the interests of all the people.

It can't be a theocracy: in a theocracy the government serves the interests of the clergy and people of faith.

I don't think it's oligarchy either: it serves the needs of a class that is not necessarily related to each other.

So the best answer is monarchy: the Royal family is central to a monarchy.