Although you ask about both the domestic and international terminals, you also suggest that both his arrival and departure flights will be from Terminal 2. That would be preferable but, it would be best to double check with his airline, as Mumbai Chhatrapati Shivaji has two terminals which are not connected, but are 5 km apart, two adjacent facilities now operated in conjunction. If your father must go between the two, there is a paid service which you might arrange for him in advance (info below).
Terminal 1 or Domestic Terminal corresponds to the old airport called Santa Cruz Airport; some locals are using this name nowadays. Terminal 2 or International Terminal is a brand new terminal and replaces the old terminal 2 that was formerly the Sahar Airport.
Both Terminals share the same runways and air facilities but are 5km far one from other, and the only option to go from one to another is using taxi or the fixed rate Inter-Terminal transportation service.
If you have a flight connection landing in T2 and departing from T1, take in mind that the transfer process will take 2-3 hours. Domestic Terminal is busiest during the day while International Terminal is busiest during night. Is not allowed to check in more than 4 hours prior your flight.
Inter terminal Transportation:
There is a paid service that connects both Domestic Terminal 1B, and International Terminal 2.
T1B to T2: Prices Rs.245 for a Sedan. Rs.700 for a SUV.
T2 to T1B: Prices Rs.230 for a Sedan. Rs.750 for a SUV.
The counters to buy the ticket are located:
T1B: Arrivals. Phone: 8767350021
T2: Level 2, International Arrivals. Phone: (022) 65882672