1. **State the problem:** Simplify the expression $4(5n+4)$. 2. **Use the distributive property:** The distributive property states that $a(b+c) = ab + ac$. Here, $a=4$, $b=5n$, and $c=4$. 3. **Apply the distributive property:** Multiply $4$ by each term inside the parentheses: $$4 \times 5n + 4 \times 4$$ 4. **Calculate each product:** $$20n + 16$$ 5. **Final simplified expression:** $$20n + 16$$ This is the simplified form of the original expression.