Step 1:

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.

Step 2:

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.

Step 3:

Thus the solution region of the given inequality is the half plane II excluding the line . It is represented by the shaded region.