Answer
Please see the graph, made using graphing software.
Work Step by Step
$3x+2y\geq12$
$3x+2y=12$
Let $x=0$
$3x+2y=12$
$3*0+2y=12$
$0+2y=12$
$2y/2=12/2$
$y=6$
Let $y=0$
$3x+2y=12$
$3x+2*0=12$
$3x=12$
$3x/3 = 12/3$
$x=4$
$(0,6)$ and $(4,0)$ are on the boundary line.
Use $(0,0)$ as the test point for shading.
$3x+2y\geq12$
$3*0+2*0 \geq 12$
$0+0 \geq 12$
$0 \geq 12$ is a false statement, so we shade the side of the line without $(0,0)$.