Answer
$\{x| x\gt6\}$
see graph.
Work Step by Step
1. Solve the left part to get $x\gt0$
2. For the right part, $\frac{4}{x}-\frac{2}{3}\lt0$ gives $\frac{12-2x}{3x}\lt0$ or $\frac{2x-12}{3x}\gt0$
3. The $\gt$ sign requires that the solution be outside of the region formed by the boundary points $(x=0, 6)$, thus the solution $x\lt0$ or $x\gt6$
4. Combine the above results to get $\{x| x\gt6\}$
5. see graph.
