You need to use simultaneous linear equations to solve for I2.
I'm not sure if this is the shortest possible method, but here's how I worked it out:
V2 = 20I2 (from ohms law) <-- this is equation #1
Also, we know that V2 = 120 - V1 , so given that V1 = 12I1 ,
then V2 = 120 - 12I1
I1 is not much good to us, so we need to express I1 in terms of I2 . Therefore I1 = I2 + I3 = I2 + 2
Substituting into above eqn, V2 = 120 - 12(I2 +2), which simplifies to
V2 = 12(8 - I2) <-- this is equation #2
Solve equations #1 and #2 simultaneously, to find that I2 is equal to 3 amps, and V2 = V3 = 60 volts.
Apply ohms law again to R3 --> R3 = 60 / 2 = 30 ohms