To find the other number, we need to divide the product by one of the numbers. The product given is \(261.36\), and one of the numbers is \(17.6\). We need to determine the other number using the formula:

\(\text{Product} = \text{First Number} \times \text{Second Number}\)

Rearranging to find the Second Number, we have:

\(\text{Second Number} = \frac{\text{Product}}{\text{First Number}}\)

Substituting the given values, we get:

\(\text{Second Number} = \frac{261.36}{17.6}\)

Perform the division:

\(\frac{261.36}{17.6} = 14.85\)

Therefore, the other number is \(14.85\).

Let's verify by multiplying back:

\(17.6 \times 14.85 = 261.36\), which confirms our calculation is correct.

Thus, the correct answer is 14.85, as none of the other options satisfy the equation.