Answer
$-\frac{5n}{12}$
Work Step by Step
By inspection, we see that the LCM of the denominators is $12$. Therefore, we create a common denominator to obtain:
$\frac{n}{6}-\frac{7n}{12}$
$=\frac{2n-7n}{12}$
$=\frac{-5n}{12}$
$=-\frac{5n}{12}$