The given inequality is $2x -3y >6$
Consider the equation $2x-3y=6$
We see taht the points $(3,0) $ and $(0,-2)$ satisfy the equation.
The graphical representation of the line is given below.
The line divides the XY -plane into two half- plane I and II .
Consider a point (0,0) in half plane I
We see that $2(0) -3(0) >6$
$0 > 6$ is false
The half plane I containing the point (0,0) is not the solution region of the inequality.
Thus the solution region of the given inequality is the half plane II excluding the line . It is represented by the shaded region.