Answer
The new capacitive reactance is $~~6.0~\Omega$
Work Step by Step
We can find an expression for the reactance of a capacitor:
$X_C = \frac{1}{\omega_d~C}$
$X_C = \frac{1}{2\pi~f~C}$
We can see that if the frequency is doubled, the reactance of the capacitor decreases by a factor of $\frac{1}{2}$
Since the original capacitive reactance was $12.0~\Omega$, the new capacitive reactance is $6.0~\Omega$
