\(|-4x-14|\ \textless \ 6 \\
-4x-14\ \textless \ 6 \ \land \ -4x-14\ \textgreater \ -6 \\
-4x\ \textless \ 6+14 \ \land \ -4x\ \textgreater \ -6+14 \\
-4x\ \textless \ 20 \ \land \ -4x\ \textgreater \ 8 \\
x\ \textgreater \ \frac{20}{-4} \ \land \ x\ \textless \ \frac{8}{-4} \\
x\ \textgreater \ -5 \ \land \ x\ \textless \ -2 \\
\boxed{x \in (-5,-2)}\)
