Integral values of an algebraic expression

Rewrite the expression as: $\frac{16n^2 + 7n + 6}{n} = 16n + 7 + \frac{6}{n}$

Since $n$ is an integer, $16n + 7$ is always an integer. For the whole expression to be an integer, $\frac{6}{n}$ must be an integer.

This implies $n$ must be an integer factor of 6. The integer factors of 6 are $\pm 1, \pm 2, \pm 3, \pm 6$.

Thus, there are 8 possible values for $n$. Since 8 is not listed in options A, B, or C, the correct choice is None of these.