1. **State the problem:** Simplify the expression $6 \div 2(1+2)$. 2. **Evaluate inside the parentheses first:** $1+2=3$. So the expression becomes $6 \div 2(3)$. 3. **Rewrite the expression:** $6 \div 2 \times 3$. According to the order of operations (PEMDAS/BODMAS), division and multiplication are performed 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:** $9$.