1. **State the problem:** Simplify the expression $$6\sqrt{6} - 4\sqrt{150}$$. 2. **Recall the rule:** To simplify radical expressions, factor the radicand (the number inside the square root) to extract perfect squares. 3. **Simplify each term:** - The first term is already simplified: $$6\sqrt{6}$$. - For the second term, factor 150: $$150 = 25 \times 6$$ So, $$4\sqrt{150} = 4\sqrt{25 \times 6} = 4 \times \sqrt{25} \times \sqrt{6} = 4 \times 5 \times \sqrt{6} = 20\sqrt{6}$$. 4. **Rewrite the expression:** $$6\sqrt{6} - 20\sqrt{6}$$ 5. **Combine like terms:** Since both terms have $$\sqrt{6}$$, subtract the coefficients: $$6\sqrt{6} - 20\sqrt{6} = (6 - 20)\sqrt{6} = -14\sqrt{6}$$. **Final answer:** $$-14\sqrt{6}$$