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,
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.
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.