1. The problem is to analyze the inequality $6 < 2x - 3y$. 2. This inequality involves two variables, $x$ and $y$, and represents a region in the coordinate plane. 3. To understand the region, first rewrite the inequality: $$6 < 2x - 3y$$ 4. Rearranging to isolate $y$: $$2x - 3y > 6$$ $$-3y > 6 - 2x$$ $$y < \frac{2x - 6}{3}$$ 5. The inequality $y < \frac{2x - 6}{3}$ describes all points below the line $y = \frac{2x - 6}{3}$. 6. The boundary line $y = \frac{2x - 6}{3}$ can be graphed to visualize the solution set. 7. The inequality is strict ($<$), so the boundary line is not included in the solution. 8. This region includes all points $(x,y)$ where $y$ is less than $\frac{2x - 6}{3}$. Final answer: The solution to the inequality $6 < 2x - 3y$ is all points $(x,y)$ such that $$y < \frac{2x - 6}{3}.$$