Answer
$\frac{4x}{x+2}$
Work Step by Step
A rational function that has a vertical asymptote at $x=-2$ is
$$
\frac{1}{x+2}
.$$
To have a horizontal asymptote at $4$, the form of the rational expression should be
$$
\frac{4\frac{x}{x}}{\frac{x}{x}+\frac{2}{x}}=\frac{4}{1+0}=4
.$$
Hence, combining the expressions above, a rational expression that has a vertical at $x=-2$ and a horizontal asymptote at $y=4$ is
$$
\frac{4x}{x+2}
.$$
