Step 1 :Find the derivative of the function f(x) and evaluate it at x = 2: \(f'(x) = 3x^2 - 12x + 12\), \(f'(2) = 0\)
Step 2 :Since the slope of the tangent line at point P is 0, the equation of the line L is \(y = 0\)
Step 3 :Solve the equation f(x) = 0: \(x^3 - 6x^2 + 12x - 8 = 0\), x = 2
Step 4 :The second point Q is the same as point P, so the distance between P and Q is \(\boxed{0}\)