1. **State the problem:** Simplify the expression $2\sqrt{3} + 4\sqrt{12} - \sqrt{48}$. 2. **Recall the rule:** To simplify expressions with square roots, factor the radicand (number inside the root) into perfect squares and simplify using $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$. 3. **Simplify each term:** - $2\sqrt{3}$ stays as is because 3 is already simplified. - $4\sqrt{12} = 4\sqrt{4 \times 3} = 4 \times 2 \sqrt{3} = 8\sqrt{3}$. - $\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}$. 4. **Rewrite the expression:** $$2\sqrt{3} + 8\sqrt{3} - 4\sqrt{3}$$ 5. **Combine like terms:** $$ (2 + 8 - 4)\sqrt{3} = 6\sqrt{3}$$ **Final answer:** $6\sqrt{3}$