Answer
$125$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( { - 1, - 2} \right)} {\left( {{x^2}y - x{y^2} + 3} \right)^3} \cr
& {\text{Evaluating the limit by direct substitution}}{\text{.}} \cr
& {\text{Substitute }} - {\text{1 for }}x{\text{ and }} - 2{\text{ for }}y \cr
& \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( { - 1, - 2} \right)} {\left( {{x^2}y - x{y^2} + 3} \right)^3} = {\left( {{{\left( { - 1} \right)}^2}\left( { - 2} \right) - \left( { - 1} \right){{\left( { - 2} \right)}^2} + 3} \right)^3} \cr
& {\text{Simplifying}} \cr
& \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( { - 1, - 2} \right)} {\left( {{x^2}y - x{y^2} + 3} \right)^3} = {\left( { - 2 + 4 + 3} \right)^3} \cr
& \mathop {\lim }\limits_{\left( {x,y} \right) \to \left( { - 1, - 2} \right)} {\left( {{x^2}y - x{y^2} + 3} \right)^3} = 125 \cr} $$