Ambiguously means in an ambiguous way: you speak, write, or act so that people can take it in more than one way. She answered ambiguously means the answer itself sat on both sides, not that she felt two feelings (that would be she felt ambivalent). It is the adverb of ambiguous, so it usually tells us how something is said or done. Fairly formal. In casual speech people more often say in a vague way or without making it clear, though those are a little looser.