Answer
$y^2=-8x$, $(-2,-4),(-2,4)$,
See graph.
Work Step by Step
1. Given the focus at $(-2,0)$, directrix $x=2$, we have $2p=4$ and $p=2$. We can write the parabola equation in a standard form $4px=-y^2$. With $p=2$, we get $y^2=-8x$
2. Let $x=-2$, we have $y^2=16$ and $y=\pm4$, thus the two points that define the latus rectum are $(-2,-4),(-2,4)$
3. See graph.