The given inequality is $ -3x +2y \geq -6$

Consider the equation $-3x +2y =-6$

We see that $(2,0) $ and $(0,-3)$ satisfy the equation.

The graphical representation of the line is given below,

Step 2:

The line divides the xy plane into two half planes I and II

Consider a point (0,0) in the half plane I.

We see that , $-3 (0) +2(0) \geq -6$

$ 0 \geq -6$ is true.

Therefore the half plane II is not the solution region.

Step 3:

Thus the solution region of the given inequality is the half plane I containing the point (0,0) including the points on the line.

It is represented by the shaded region.