How do you factor -r ^ { 4} + 2r ^ { 3} - 6r ?

$- r \left({r}^{3} - 2 {r}^{2} + 6\right)$
In this expression, the only thing in common is $- r$ or $- 1$ and $r$. This means that we can factor out a $- 1$ and $r$:
$- r \left({r}^{3} - 2 {r}^{2} + 6\right)$