Given the polynomial \( P(x) = x^3 - 3x^2 - 4x + 12 \), let \( Q(x) = P(x - 2) \). Factorize \( Q(x) \) completely. Then, use the roots of \( Q(x) \) to determine the perimeter of a rectangle where the length is the sum of the roots of \( Q(x) \) and the width is the product of the roots of \( Q(x) \). What is the perimeter of the rectangle? Let's think step by step and output the final answer within \boxed{}.
user