Answer
The equivalent inductance is $~~59.3~mH$
Work Step by Step
We can find the equivalent inductance of $L_2$ and $L_3$ which are in parallel:
$\frac{1}{L_{23}} = \frac{1}{L_2}+\frac{1}{L_3}$
$\frac{1}{L_{23}} = \frac{1}{50.0~mH}+\frac{1}{20.0~mH}$
$\frac{1}{L_{23}} = \frac{2}{100.0~mH}+\frac{5}{100.0~mH}$
$L_{23} = 14.3~mH$
We can find the equivalent inductance of $L_1, L_{23},$ and $L_4$ which are in series:
$L_{eq} = 30.0~mH+14.3~mH+15.0~mH = 59.3~mH$
The equivalent inductance is $~~59.3~mH$
