for diatomic molecule -
Number of translational axies contributes in kinetic energy = 3
each contribute with $\frac{1}{2}\mathrm{KT}$ Kinetic energy

So, average translational Kinetic energy

$=3\times \frac{1}{2}\mathrm{kT}$

$=\frac{3}{2}\mathrm{kT}----\left(\mathrm{I}\right)$

There are two rotational axis contributes in Kinetic energy with value $\frac{1}{2}\mathrm{kT}$ each,
so

total rotational thetis energy $=2\times \frac{1}{2}\mathrm{kT}$

$=\frac{2}{2}\mathrm{kT}\text{----(II)}$

Now, ratio of average translational kinetic energy and average rotational kinetic energy is

$=\frac{\frac{3}{2}\mathrm{KT}}{\frac{2}{2}\mathrm{KT}}=\frac{3}{2}$

Hence option D is correct.