This is an interesting question because it looks from the statistics like more people are getting this one wrong than right. And furthermore the people who are answering correctly are doing so in (as of January 2nd) about 35 seconds. And those who are missing it are taking about 4 times as long.

This indicates a question that is a classic case of what I call "pure vocabulary." If you happen to know all 6 words you are probably going to get this right very quickly. If you do not know at least 5 of 6 then you are perhaps going to take longer and still produce an incorrect answer.

The context for this question is fairly simply to put together. The first blank mentions something that is rare for politicians. A quick thought of the nature of politicians will remind us that it is not rare for them to embrace the center stage! So the first blank needs to be something about surrendering the center stage. The word that works here is "foresake." Which does mean to relinquish. So in other words "foresake the center stage" means not have to be the center of attention.

For the second blank we need something that means not being the center of attention. We can use process of elimination. If you know the word "garrulous" then you will perhaps discern that "garrulity" means to talk too much. This is the exact opposite of what we want. So choice D is out. Choice E is "misanthropy" - "anthropy" means humans and misanthropy is a dislike of humans. Surely this is not something we want in a politician!

So by elimination we can pick Choice F "self-effacement" which means making yourself inconspicuous. Obviously this is the opposite of "center of attention."

Many GRE questions will require more work to understand the context, but some like this one will be mostly a matter of vocab!