$x < −3 \text{ or } x > 3$

Begin by changing the inequality to an equation and solve for the boundary points.

$\left|3x-2\right|=2$

Since$\left|±2\right| = 2$, this can be rewritten as two equations. Solve the two equations for $x$ and plot the boundary points on a number line.
$3x − 2 = 2 \quad \quad 3x − 2 = −2$

Test points on the number line in the original inequality to find the regions that make it true. Shade them and describe them algebraically.

$4x − 2 = 10 \quad \quad 4x − 2 = −10$

Look inside. The cube root of $8$ is $2$.