～ていただけませんかWon't you, Could you please (Humble request)

ていただけませんか is the humble speech form of てもらえませんか, which itself is the negative potential form of てもらう 'to have (A) done by someone else'.

This structure is a combination of て (the conjunction particle), the う-Verb いただく 'to be topped with', the polite-negative auxiliary verb ません, and the question particle, か.

Generally, it is translated in a similar way as てもらえませんか 'won't you (A)', or 'could you please (A)'.

This construction and いただく itself can regularly be seen as 頂(いただ)く, its kanji form. Due to this kanji literally meaning 'to be topped with', it is just acknowledging that the person that is doing the action for you (or someone in your group), is doing so from 'above' (sounds more respectful).

Here we can see how the 'to be topped/capped with' meaning is used in a standard sentence.