Answer
a) $0.239H$
b) $120Hz$
Work Step by Step
a) $X_{L}=90 Ohm$ $f=60Hz$
$X_{L}=2\times pi \times f\times L$
Thus, $L=\frac{90}{2\times3.14\times60}=0.239H$
b) As $X_{L}$ is directly proportional to f, to double the reactance, we have to double the frequency as well. i.e. $120Hz$