#### Answer

$$10$$

#### Work Step by Step

Given
$$\lim _{(x, y) \rightarrow(2,-1)}\left(x y-3 x^{2} y^{3}\right)$$
Since $ \left(x y-3 x^{2} y^{3}\right)$ is a continuous polynomial function, then by substitution, we get
\begin{align*}
\lim _{(x, y) \rightarrow(2,-1)}\left(x y-3 x^{2} y^{3}\right)&=\lim _{(x, y) \rightarrow(2,-1)}\left((2) (-1)-3 (2)^{2} (-1)^{3}\right)\\
&=-2+12=10
\end{align*}