Identify the given equation of the parabola and the point it passes through.

The equation of the parabola is $ص^2 = 2س$ (which is $y^2 = 2mx$ in English notation).
The parabola passes through the point $(-2, 4)$, meaning $س = -2$ and $ص = 4$.

Substitute $y = 4$ and $x = -2$ into $y^2 = 2mx$:

Divide both sides by $-4$:

The value of $m$ is $-4$.

Comparing this with the given options:
1: $-2$
2: 2
3: 4
4: $-4$

The correct option is 4.