Figure shows the combination of inductances and capacitances. Resonant frequency of the L - C circuit is

Resonant frequency analysis

The series combination of inductors $L$ and $2L$ yields equivalent inductance $L_{eq} = L + 2L = 3L$.

The parallel combination of capacitors $C$ and $2C$ gives equivalent capacitance $C_{eq} = C + 2C = 3C$.

The resonant frequency follows from $f_0 = \frac{1}{2\pi\sqrt{L_{eq}C_{eq}}}$.

Substituting gives $f_0 = \frac{1}{2\pi\sqrt{9LC}} = \frac{1}{6\pi\sqrt{LC}}$.

This corresponds to option D.