Answer
The inductor and the capacitor have the same reactance when the frequency is $~~650~Hz$
Work Step by Step
We can equate the reactances to find $\omega_d$:
$V_L = V_C$
$I~X_L = I~X_C$
$I~\omega_d~L = \frac{I}{\omega_d~C}$
$\omega_d^2 = \frac{1}{L~C}$
$\omega_d = \sqrt{\frac{1}{L~C}}$
$\omega_d = \sqrt{\frac{1}{(6.0\times 10^{-3}~H)(10\times 10^{-6}~F)}}$
$\omega_d = 4082.5~rad/s$
We can find the frequency:
$f = \frac{\omega_d}{2\pi} = \frac{4082.5~rad/s}{2\pi} = 650~Hz$
The inductor and the capacitor have the same reactance when the frequency is $~~650~Hz$
