In the given question, the cross is between YYRRII and yyrrii. The ${\mathrm{F}}_1$ hybrid is YyRrIi.

For getting, the ${\mathrm{F}}_2$ generation the cross is YyRrIi x YyRrIi. It is a pea plant where all characters are independent assorted so we can consider the crosses separately:

In $\mathrm{Y}\mathrm{y}\mathrm{ }\mathrm{x}\mathrm{ }\mathrm{Y}\mathrm{y}$ , the proportion of yellow seeds produced is $\frac{3}{4}$ and the proportion of green seeds produced is $\frac{1}{4}$

In $\mathrm{R}\mathrm{r}\mathrm{ }\mathrm{x}\mathrm{ }\mathrm{R}\mathrm{r}$ , the proportion of round seeds produced is $\frac{3}{4}$ and the proportion of wrinkled seeds produced is $\frac{1}{4}$

In Ii x Ii, the proportion of inflated pods produced is $\frac{3}{4}$ and the proportion of constricted pods produced is $\frac{1}{4}$

Thus the proportion of plants having green round seeds in an inflated pod in the ${\mathrm{F}}_2$ generation is $\frac{1}{4}\times \frac{3}{4}\times \frac{3}{4} =\frac{9}{64}$