Please don't forget to return that book to the library.
Literal
Not-forget-[without-ず] that book [object-を] library [dat-に] return-[polite-request-てください]
Standard double-object structure: 本を returned 図書館に. に here marks the destination/goal of 返す, analogous to 'to' in English. 返す is the transitive 'return', as opposed to the intransitive 返る.