Technically.....f(x) does NOT have a minimum at x = -8 [ if I remember my Calculus correctly ]
A local minimum cannot occur at an endpoint of a function......only an absolute max or min can occur at an endpoint
So..... at x = -8 we cannot have an absolute min since we have an absolute min at x = 6 and no local minimum at any point on the graph
This might help : http://tutorial.math.lamar.edu/Classes/CalcI/MinMaxValues.aspx