。
Do you know what colour she likes?
Literal
She [topic-は] what kind colour [subject-が] like [question-か] know [question-か]?
Another doubled-か structure: the embedded question (どんな色がすきか) and the outer question (知っていますか). 知っている ('know,' literally 'is in the state of having come to know') is another ~ている of resulting state — the related 知る on its own (without ~ている) is comparatively rare and means 'come to know, learn,' while the everyday 'I know' is always 知っている. Negative 'don't know' is correspondingly 知らない (the bare negative form), since 知っていない is awkward.