To find the domain of any rational function, we need to determine where the denominator is zero. The best way to find these values exactly is to factor the denominator. Thus, we observe that
\begin{equation*}
2x^3 - 6x^2 - 8x = 2x(x^2 - 3x - 4) = 2x(x+1)(x-4)\text{.}
\end{equation*}
By the Zero Product Property, it follows that the denominator of \(r\) is zero at \(x = 0\text{,}\) \(x = -1\text{,}\) and \(x = 4\text{.}\) Hence, the domain of \(r\) is the set of all real numbers except \(-1\text{,}\) \(0\text{,}\) and \(4\text{.}\)