In $LCR$ series circuit, resonance frequency $f_{0}$ is given by:
$L \omega=\frac{1}{ C \omega}$
$\Rightarrow \omega^{2}=\frac{1}{ LC }$
$\therefore \omega=\sqrt{\frac{1}{ LC }}=2 \pi f _{0}$
$\therefore f _{0}=\frac{1}{2 \pi \sqrt{ LC }} $
$d \Rightarrow f _{0} \propto \frac{1}{\sqrt{ C }}$
When the capacitance of the circuit is made $4$ times, its resonant frequency become $f _{0}'$
$\therefore \frac{ f _{0}'}{ f _{0}}=\frac{\sqrt{ C }}{\sqrt{4 C }}$
$\Rightarrow f _{0}'=\frac{ f _{0}}{2}$