Answer
$\left( \dfrac{2}{3}, 2\right)$
Work Step by Step
Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x \lt a$ then the solution to the given inequality, $
\left| 3x-4 \right|\lt 2
,$ is
\begin{array}{l}\require{cancel}
-2\lt 3x-4\lt 2
\\\\
-2+4\lt 3x-4+4\lt 2+4
\\\\
2\lt 3x\lt 6
\\\\
\dfrac{2}{3}\lt \dfrac{3x}{3}\lt \dfrac{6}{3}
\\\\
\dfrac{2}{3}\lt x\lt 2
.\end{array}
Hence, the solution set is the interval $
\left( \dfrac{2}{3}, 2\right)
.$