。
She may have known the answer.
Literal
She [topic-は] answer [object-を] knew [explanatory-のかもしれない].
~のかもしれない wraps the preceding clause (答を知っていた) with the explanatory の before かもしれない, adding a nuance of 'it might be the case that...' — slightly more reflective than bare かもしれない. The speaker is speculating about a past situation with a hint of discovering a possibility. 答 rather than 答え uses the on'yomi reading.