1. **State the problem:** Simplify the expression $2(4x+1)9$. 2. **Understand the expression:** The expression involves multiplication of $2$, the quantity $(4x+1)$, and $9$. 3. **Use the associative property of multiplication:** We can multiply the constants first: $2 \times 9 = 18$. 4. **Rewrite the expression:** $$2(4x+1)9 = 18(4x+1)$$ 5. **Distribute $18$ over the terms inside the parentheses:** $$18 \times 4x + 18 \times 1 = 72x + 18$$ 6. **Final simplified expression:** $$72x + 18$$ This is the simplified form of the original expression.