The correct answer is B) back away a few lengths to clear the buoy and then go ahead on the engines. This is the correct procedure when casting off from a mooring buoy in calm weather. By backing away a few lengths, you ensure that the vessel clears the mooring buoy before going ahead on the engines. This helps avoid fouling the propeller or damaging the vessel or the buoy. Going half ahead and passing upstream (A) or putting the rudder hard right (C) are not the proper techniques in this situation. Going full ahead (D) on the engines without first clearing the buoy could result in a collision or damage.