これを預かってもらえますか。

this (indicating an item near the speaker, the action of the speaker, or the current topic); this person (usu. indicating someone in one's in-group); now; here; I (me); certainly

indicates direct object of action; indicates subject of causative expression; indicates an area traversed; indicates time (period) over which action takes place; indicates point of departure or separation of action; indicates object of desire, like, hate, etc.

to look after; to take care of; to keep; to hold on to; to keep in custody; to take charge of; to be entrusted with; to receive on deposit; to reserve (judgment); to leave undecided

indicates a question (sometimes rhetorical); or; whether or not; some- (e.g. something, someone); indicates doubt, uncertainty, etc.; emphatic prefix; suffix forming adjectives or adverbs; in that way