For some reason I don't get this at all. I understand ellipses and hyperbolas, but not a simple parabola.
The parabola takes on the form $\displaystyle y^2=4px$
Since our equation is $\displaystyle y^2=-6x$, comparing it to the standard form we see that $\displaystyle 4p=-6$, solving for p, we get $\displaystyle p=-\frac{3}{2}$. Thus, that's how they get $\displaystyle -6x=4\left(-\frac{3}{2}\right)x$
Does that make sense?
--Chris