。
Could I borrow a blanket?
Literal
Blanket [object-を] lend-[humble-receive-have-[can-ますか]].
~ていただけますか is the most polite way to ask someone to do something — built from the humble auxiliary ~ていただく in its potential form (いただける). The ます form + か makes it a polite question. Literally something like 'could I humbly receive your lending?' — translated as the English 'could you please lend me X.' Classroom politeness gold standard.