The area $$A$$ and height $$h$$ of an equilateral triangle with side length $$s$$ are given by the formulas $$ A = \frac{\sqrt{3}}{4}s^2 $$ and $$ h = \frac{\sqrt{3}}{2}s $$. At the instant when the side length is $$s = 8$$ centimeters, the area is increasing at a rate of $$12\sqrt{3}$$ square centimeters per second. At what rate is the height of the triangle increasing at that instant, in centimeters per second?