See figure and explanations.
Work Step by Step
Step 1. Find the solutions of $3x+y\leq6$ (originally red shaded). Step 2. Find the solutions of $2x-y\leq-1$ (originally blue shaded). Step 3. Find the solutions of $x\gt-2$ (originally green shaded). Step 4. Find the solutions of $y\lt4$ (originally purple shaded). Step 5. The solutions for the system of inequalities can be found as the overlap of the above solutions, shown with the darkest region (labeled solution region, four-side shaped) in the figure.