1. **State the problem:** Simplify the expression $2\sqrt{48} - \frac{6}{\sqrt{3}}$. 2. **Recall the rules:** - Simplify square roots by factoring out perfect squares. - Rationalize denominators when necessary. 3. **Simplify $2\sqrt{48}$:** $$\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$$ So, $$2\sqrt{48} = 2 \times 4\sqrt{3} = 8\sqrt{3}$$ 4. **Simplify $\frac{6}{\sqrt{3}}$ by rationalizing the denominator:** Multiply numerator and denominator by $\sqrt{3}$: $$\frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{6\sqrt{3}}{3} = 2\sqrt{3}$$ 5. **Combine the terms:** $$8\sqrt{3} - 2\sqrt{3} = (8 - 2)\sqrt{3} = 6\sqrt{3}$$ **Final answer:** $$6\sqrt{3}$$