1. **State the problem:** Simplify the expression $2^2\sqrt{6} - 2^2\sqrt{24}$. 2. **Recall the formula and rules:** - $2^2 = 4$. - Simplify square roots by factoring out perfect squares. 3. **Rewrite the expression:** $$4\sqrt{6} - 4\sqrt{24}$$ 4. **Simplify $\sqrt{24}$:** $$\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}$$ 5. **Substitute back:** $$4\sqrt{6} - 4(2\sqrt{6}) = 4\sqrt{6} - 8\sqrt{6}$$ 6. **Combine like terms:** $$4\sqrt{6} - 8\sqrt{6} = (4 - 8)\sqrt{6} = -4\sqrt{6}$$ **Final answer:** $$-4\sqrt{6}$$