Find the product. Simplify your answer. \[ (4 y+4)(y+4) \] \( \square \)

To find the product \((4y + 4)(y + 4)\), we can use the distributive property (or FOIL method). First, distribute \(4y\) to both terms in the second parenthesis: \[ 4y \cdot y = 4y^2 \quad \text{and} \quad 4y \cdot 4 = 16y. \] Next, distribute \(4\) to both terms in the second parenthesis: \[ 4 \cdot y = 4y \quad \text{and} \quad 4 \cdot 4 = 16. \] Now, combine all the terms together: \[ 4y^2 + 16y + 4y + 16 = 4y^2 + 20y + 16. \] So the simplified product is: \[ \boxed{4y^2 + 20y + 16}. \]