1. **State the problem:** Simplify the expression $$\sqrt{3}(\sqrt{24} - \sqrt{6})$$. 2. **Recall the property of square roots:** $$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$$. 3. **Apply the property to each term:** $$\sqrt{3} \times \sqrt{24} = \sqrt{3 \times 24} = \sqrt{72}$$ $$\sqrt{3} \times \sqrt{6} = \sqrt{3 \times 6} = \sqrt{18}$$ 4. **Rewrite the expression:** $$\sqrt{72} - \sqrt{18}$$ 5. **Simplify each square root by factoring out perfect squares:** $$\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$$ $$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$$ 6. **Substitute back:** $$6\sqrt{2} - 3\sqrt{2}$$ 7. **Combine like terms:** $$6\sqrt{2} - 3\sqrt{2} = (6 - 3)\sqrt{2} = 3\sqrt{2}$$ **Final answer:** $$3\sqrt{2}$$