Ugh.
Ask a bad question...
I'm a British English speaker, so to me neither of these options are "good" sentences. Also, neither of them are "wrong" either, but they sound like something a non-native speaker would write. Note that I'm talking only about writing here - native speakers say both of these things all the time, but speech is always more grammatically fluid than writing, and I'd get the intended meaning from intonation.
I think the root of the problem is that it's not even clear what the sentence should mean. If it's the most logical "completion of brushing your teeth is a prerequisite for eating and enjoying your breakfast", then the correct written form is:
- Brush your teeth first, and then you can enjoy breakfast
American English speakers please correct me, but I believe this is natural in both British and American writing.
The problem is that the question-setter hasn't given you this answer as one of the choices, so you're left with the dubious task of choosing the "least bad" answer.
If this was a piece of speech, the "and then" could be elided two ways: either drop and, or drop then, and this will give you your two possible answers, but it's worth noting that they now have two slightly different meanings, and both have problems:
A. Brush your teeth first, and you can enjoy breakfast. - less consequential: the act of brushing your teeth allows you to get more enjoyment from your breakfasts; you've lost the "prerequisite" sense.
C. Brush your teeth first, then you can enjoy breakfast - this emphasises the consequence: you're not going to be allowed to enjoy your breakfast until you've brushed your teeth. But here the comma is also wrong: it should be a semicolon.
As a British English speaker, I think C is "less bad" than A, but really neither of them is a good written sentence. Also, I'm assuming that consequence was what the original sentence was trying to convey. Maybe it wasn't.
So you've been left to second-guess what the question-setter actually meant to ask you, which sucks.