…ていただけませんか
…て…
いただけませんか: Used with the te-form of a verb. More appropriate than ください when you request a favor from a nonpeer or from a stranger.
くれませんか: Used with the te-form of a verb. Roughly the same as ください. Most appropriate in the host-family context.
くれない？: Used with the te-form of a verb. Asks for a favor in a very casual way. This is good for speaking with members of your peer group.