。
Please tell me a place where I can read books.
Literal
Books [subject-が] can-read place [object-を] teach-[please-てください].
読める is the potential form of 読む. Inside a relative clause modifying 場所 ('place'), the subject が marks 'books' and the potential 'can be read' describes a feature of the place. 教える here means 'to tell, inform,' not 'to teach academically' — a common conversational meaning.