1. **State the problem:** Solve the equation $$2(3+m) = n$$ for $n$ in terms of $m$. 2. **Formula and rules:** Use the distributive property to expand the left side: $$a(b+c) = ab + ac$$. 3. **Apply distributive property:** $$2(3+m) = 2 \times 3 + 2 \times m = 6 + 2m$$ 4. **Rewrite the equation:** $$6 + 2m = n$$ 5. **Express $n$ explicitly:** $$n = 6 + 2m$$ **Explanation:** We expanded the left side by multiplying 2 with each term inside the parentheses. Then, we isolated $n$ on one side to express it in terms of $m$. **Final answer:** $$n = 6 + 2m$$