Hmmm... I would say neither.

Neither. Synonyms of brisk might be quick, rapid, fast, sharp. Agile and nimble both refer a lot more to flexibility

I agree with Gary. NEITHER word is a synonym of "brisk", in any context. "Nimble" and "agile" have a similar meaning - they both describe a person who can move easily and smoothly. "Nimble" has the added connotation of speed, while "agile" suggests flexibility. "Brisk" does not describe a person, but a way of doing something, particularly walking. It means "quick", as in "A brisk walk every morning is good for your heart". You cannot use either of the suggested words in the place of "brisk". I suspect that whoever devised this fundamentally flawed question intended the answer to be "nimble", as both words suggest a speed of movement. But they are not synonyms. You can't be a brisk person or take a nimble walk. Even as adverbs, the meaning is different - moving nimbly and moving briskly are not the same thing. The mere fact that two words appear in the same thesaurus entry does not mean that they are synonymous.

Brisk means to do something quite quickly. We mainly use it to describe the way we walk. In the winter I go for a brisk walk because it's too cold to walk slowly. Agile and nimble means how flexible someone is when doing a physical activity, for example rock-climbing.