It is much rarer for answers to be downvoted than for questions -- the predominant culture here is to comment when an answer has an error, rather than to silently downvote. Here are a few reasons I might downvote your answer without comment:
It shows a lack of presentation effort: there are spelling/capitalization errors, math is not Latexed, etc. I would guess this is the reason your recent answer got the downvote.
The answer is wrong. Usually I will comment and point out the error, but if the error is egregious (suggests a hopelessly wrong approach, for instance), or you didn't respond to another user's comment in a timely manner, I might downvote instead.
The question asks for a hint, and you spoil the full solution.
If you want to ask, in a comment to your question, why you received the downvote, it is OK to do so. But you won't always get an answer.