Answer
$$2$$
Work Step by Step
Given $$ \lim _{(x, y) \rightarrow\left(\frac{4}{9}, \frac{2}{9}\right)} \frac{x}{y}$$
Since $\frac{x}{y}$ is a rational function and is continuous at $ \left(\frac{4}{9}, \frac{2}{9}\right)$, then by using substitution, we get
\begin{align*}
\lim _{(x, y) \rightarrow\left(\frac{4}{9}, \frac{2}{9}\right)} \frac{x}{y}&= \frac{4/9}{2/9}\\
&=\frac{4}{2}\\
&=2
\end{align*}