$x = - 3$ is an equation that passes through $\left(- 3 , 4\right)$ and is perpendicular to $y = - 2$.
The equation $y = - 2$ is going to create a horizontal (slope $= 0$) line that passes through the point $\left(0 , - 2\right)$. To create a line that is perpendicular to that line, you need to create a line that is vertical (no slope).
However, the line also needs to pass through the point $\left(- 3 , 4\right)$. so the only equation that works is $x = - 3$.