1. **State the problem:** Simplify the expression $6 \div 2(1+2)$. 2. **Evaluate inside the parentheses:** Calculate $1+2=3$. Now the expression is $6 \div 2(3)$. 3. **Rewrite the expression:** $6 \div 2 \times 3$. According to the order of operations, division and multiplication have the same precedence and are evaluated from left to right. 4. **Perform division first:** $6 \div 2 = 3$. Now the expression is $3 \times 3$. 5. **Perform multiplication:** $3 \times 3 = 9$. 6. **Final answer:** The value of $6 \div 2(1+2)$ is $9$.