。
Could I make a reservation?
Literal
Reservation [object-を] can-I-request-[polite-ますか]?
お願いできますか is the potential form of お願いする ('to request humbly') in polite ~ます form — literally 'can I humbly request.' An extremely common polite request opener, slightly softer than お願いします because it frames the request as a question rather than a statement.