1. **State the problem:** Multiply the radical expression $\sqrt{3}(\sqrt{12} + 4)$. 2. **Recall the distributive property:** $a(b + c) = ab + ac$. We will apply this to multiply $\sqrt{3}$ by each term inside the parentheses. 3. **Apply the distributive property:** $$\sqrt{3} \times \sqrt{12} + \sqrt{3} \times 4$$ 4. **Multiply the radicals:** Recall that $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$. So, $$\sqrt{3} \times \sqrt{12} = \sqrt{3 \times 12} = \sqrt{36}$$ 5. **Simplify $\sqrt{36}$:** $$\sqrt{36} = 6$$ 6. **Multiply $\sqrt{3}$ by 4:** $$\sqrt{3} \times 4 = 4\sqrt{3}$$ 7. **Combine the results:** $$6 + 4\sqrt{3}$$ **Final answer:** $$6 + 4\sqrt{3}$$