Step 1:

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

Consider the equation $2x+y=6$

We observe that $(3,0) $ and $(0,6)$

Satisfy the equation

The graphical representation of the line $2x+y=6$ is

Step 2:

The Line divides the xy- plane into two half plane I and II select a point not on the line say (0,0)

We see that $2(0) +0 \geq 6$ is false .

Therefore half plane I containing point (0,0) is not the solution of the given inequality

Step 3:

The solution region of the given inequality is the shaded half including the line.