Resonance frequency of an L-C circuit is the frequency when the intensity of current is maximum in the circuit.

Resonant frequency, $f=\frac{1}{2\pi \sqrt{LC}}$

$f\propto \frac{1}{\sqrt{C}}$ or $\frac{f_1}{f_2}=\sqrt{\frac{C_2}{C_1}}$

Now, if the capacitance is made four times the initial value,

$\frac{f}{f_2}=\sqrt{\frac{4C}{C}}\Rightarrow f_2=\frac{f}{2}$