Final answer:
The FD SYNC button can adjust the flight director modes of NAV, IAS/MACH, VS, ALT, and HDG.
Step-by-step explanation:
The FD SYNC button is used to synchronize flight director modes with the current aircraft state or pilot inputs. When discussing which flight director modes can be adjusted using the FD SYNC button, the correct answer is option a) NAV, IAS/MACH, VS, ALT, HDG. These modes represent navigation, indicated airspeed or Mach number, vertical speed, altitude hold, and heading, respectively. Each of these modes helps the pilots manage the aircraft's flight path and adherence to a flight plan or air traffic control instructions.