Find the product. Simplify your answer. \[ (3 p+3)(p+4) \]

To find and simplify the product \( (3p + 3)(p + 4) \), we can use the distributive property, often referred to as the FOIL method for binomials. First, distribute \( 3p \) to both terms inside the second parenthesis: \[ 3p \cdot p + 3p \cdot 4 = 3p^2 + 12p. \] Next, distribute \( 3 \) to both terms inside the second parenthesis: \[ 3 \cdot p + 3 \cdot 4 = 3p + 12. \] Now, combine all these terms together: \[ 3p^2 + 12p + 3p + 12. \] Combine the like terms \( 12p \) and \( 3p \): \[ 3p^2 + 15p + 12. \] Thus, the simplified expression for the product \( (3p + 3)(p + 4) \) is: \[ \boxed{3p^2 + 15p + 12}. \]