Step 1 :Find the first and second derivatives of the function: $y' = 3x^2 - 16x - 12$ and $y'' = 6x - 16$.
Step 2 :Determine the critical points by setting $y'$ equal to zero: $3x^2 - 16x - 12 = 0$. The critical points are $x = -\frac{2}{3}$ and $x = 6$.
Step 3 :Determine the inflection points by setting $y''$ equal to zero: $6x - 16 = 0$. The inflection point is $x = \frac{8}{3}$.
Step 4 :Analyze the first and second derivatives to determine the relative maxima, relative minima, and points of inflection.
Step 5 :Relative maxima: $(-\frac{2}{3}, 6.148)$
Step 6 :Relative minima: $(6, -142)$
Step 7 :Points of inflection: $(\frac{8}{3}, -67.926)$
Step 8 :\(\boxed{\text{Relative maxima: }(-\frac{2}{3}, 6.148)}\)
Step 9 :\(\boxed{\text{Relative minima: }(6, -142)}\)
Step 10 :\(\boxed{\text{Points of inflection: }(\frac{8}{3}, -67.926)}\)