2. Given the lengths of the three altitudes of $\triangle A B C$ are $\frac{2}{n+6} 、 \frac{1}{3 n+12} 、 \frac{1}{8-2 n}$. Then the range of values for $n$ is
$$
\left\{
\begin{array}{l}
-\frac{14}{11}(16-4 n) S, \\
(6 n+24) S+(16-4 n) S>(n+6) S, \\
(n+6) S+(16-4 n)>(6 n+24) S .
\end{array}\right.
$$

Solving yields $-\frac{14}{11}<n<-\frac{2}{9}$.