。
Could you bring me a pillow and blanket?
Literal
Pillow [and-と] blanket [object-を] bring-[can I receive-ていただけるか]?
持ってくる is the compound 'bring,' and いただける is the polite potential of いただく (humble 'receive'). ~ていただけるか ('could I have you X for me?') is a very polite request form, more deferential than ~てください. The humble form lowers the speaker relative to the listener.