The verbal expression "the sum of 15 and the product of a number and 4" can be translated into the algebraic expression as follows:
- The "product of a number and 4" refers to \(4n\), where \(n\) is the number.
- The "sum of 15 and" indicates that you should add 15 to this product.
Therefore, the correct algebraic expression is:
\[ 15 + 4n \]
None of the options you provided match this expression directly.