Find all the values of x where the tangent line is horizontal.

2x^3+36x^2+192x+12

At x = - 4 and - 8

Take the derivative of the given equation to find rate of change of the graph.

f' (x) = 6x^2 + 72x + 192

At a horizontal tangent, f' (x) = 0, so set the equation equal to 0 and solve. Eventually you get x = - 4 and - 8