The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes $n = 2 \to n = 3$ and $n = 4 \to n = 6$ transitions, respectively, is:
$\dfrac{1}{\lambda}\propto\left(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}\right)$. For $2\to3$: $\tfrac{5}{36}$; for $4\to6$: $\tfrac{5}{144}$. $\dfrac{\lambda_{2\to3}}{\lambda_{4\to6}} = \dfrac{5/144}{5/36} = \dfrac{1}{4}$.