#x=-3# is an equation that passes through #(-3,4)# and is perpendicular to #y=-2#.

Explanation:

The equation #y=-2# is going to create a horizontal (slope #=0#) line that passes through the point #(0,-2)#. 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 #(-3,4)#. so the only equation that works is #x=-3#.