$\begin{align}  & {{(2x-3y)}^{7}} \\ & \text{The general expansion formula will be}{{\text{ }}^{7}}{{C}_{r}}{{(2x)}^{r}}{{(-3y)}^{n-r}} \\ & \text{The term having }{{x}^{3}}{{y}^{4}}\text{ will be when }r=3 \\ & {{\therefore }^{7}}{{C}_{3}}{{(2x)}^{3}}{{(-3y)}^{4}}=35(8{{x}^{3}})(81{{y}^{4}})=22680{{x}^{3}}{{y}^{4}} \\ & \text{The coefficient of }{{x}^{3}}{{y}^{4}}\text{ is 22680} \\\end{align}$