Inductor with constant current source
Ignoring a few things that make this circuit largely impractical like: -


How can a switch in series with a current source interrupt current
The infinite voltage present across both inductors at t = 0
There will be resistive losses in the coils
The resistor (it is a red herring)


You are left with the basic fact that current is shared betweeen the two inductors (3 H and 2 H) inversely proportional to their inductance. So the 2 H inductor takes 1.5 times the current of the 3 H inductor and this means that \$I_2\$ = 6 amps.

Previously I said 6.6667 amps but that was a stupid thing to say and was a brain-fart.

In the fullness of time, the voltage across the coils would drop to zero and the current share would be determined by the inductor's respective DC resistances but the question is about \$I_2(0^+)\$ and not what happens after several seconds or minutes or hours.