I'm trying to isolate $y$. I have a constant times a negative one? Do I ignore the negative and leave is as a constant? Here's what I'm working with...
$$|(6-2(y^3))| = ke^{-3\times2}$$
For a positive portion: $6-2(y^3) = ke^{-3\times-2}$
For negative portion: $6-2(y^3) = -ke^{-3\times-2}$
Does the negative portion just simplify to $ke^{-3\times-2}$ ? I don't understand the rules of constants...
You have to take into account the sign of $k$. In the positive case, you have $K>0$ since exponential is always positive, in the other you have $-k <0$ which is again $k>0$. You can simplify this to just $k e^{-3x-2}$ as you said, but then you have $k<0$.