Answer
The current in inductor 1 is $~~0.75~A$
Work Step by Step
When the circuit is in a steady state, the inductors act like ordinary wires. All of the current in the circuit will flow around the outside loop and no current will flow through $R_2$
We can find the current in the circuit:
$i = \frac{\mathscr{E}}{R_1}$
$i = \frac{6.0~V}{8.0~\Omega}$
$i = 0.75~A$
The current in inductor 1 is $~~0.75~A$
