1. Stating the problem: We need to evaluate the expression $$\sqrt{(-2\sqrt{3} - 2\sqrt{3})^2}$$. 2. Simplify inside the parentheses: Combine like terms. $$-2\sqrt{3} - 2\sqrt{3} = -4\sqrt{3}$$ 3. Substitute back into the expression: $$\sqrt{(-4\sqrt{3})^2}$$ 4. Square inside the square root: $$(-4\sqrt{3})^2 = (-4)^2 \times (\sqrt{3})^2 = 16 \times 3 = 48$$ 5. Now the expression is: $$\sqrt{48}$$ 6. Simplify the square root: $$\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$$ 7. Final answer: $$\boxed{4\sqrt{3}}$$