1. **State the problem:** Simplify the expression $$\frac{12 \sqrt{60}}{3 \sqrt{5}}$$. 2. **Recall the rules:** - Simplify square roots by factoring out perfect squares. - When dividing fractions, divide the coefficients and the radicals separately. - Use the property $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$. 3. **Simplify the coefficients:** $$\frac{12}{3} = \cancel{\frac{12}{3}} = 4$$ 4. **Simplify the radicals:** $$\frac{\sqrt{60}}{\sqrt{5}} = \sqrt{\frac{60}{5}} = \sqrt{12}$$ 5. **Simplify $$\sqrt{12}$$:** $$\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2 \sqrt{3}$$ 6. **Combine the simplified parts:** $$4 \times 2 \sqrt{3} = 8 \sqrt{3}$$ **Final answer:** $$8 \sqrt{3}$$