is very close to the Riverside “D” branch of the Green Line, which should take you right into North Station where the TD Garden is. (If your train’s last stop turns out to be at Park Street or Government Center, just wait on the platform for a train marked North Station or Lechmere, and get off that train at North Station.)
This is a hotel in Braintree which may or may not have shuttle service to the Red Line in Quincy or Braintree. You would have to ride the Red Line to get to the Green Line. I’d advise calling the hotel to find out. There is an airport shuttle station close by to this hotel.
I do NOT recommend that you use the Motel 6 in Braintree which is walking distance from the Braintree Red Line station. This particular Motel 6 has a bad reputation for drug activity and other crime.