The top of the lampshade has diameter $6$, so its radius is $3$. The bottom has diameter $8$, so its radius is $4$.

The ratio of the areas of the two circles:

$\frac{\text{Top area}}{\text{Bottom area}} = \frac{\pi(3)^2}{\pi(4)^2} = \frac{9}{16}$

The ratio is $9:16$.