Answer
Please see the graph.
Work Step by Step
Orange line: $2x-3y\le6$
Purple line: $y\ge0$
Red line: $y\le4$
Blue line: $x\ge0$
To determine what side of the line to shade, we use a point not on the line. We can use $(1,1)$ for four of the lines.
Orange line:
$2x-3y\le6$
$2*1-3*1\le6$
$2-3\le 6$
$-1 \le 6$ (true, so we shade the left side of the line)
Purple line:
$y\ge 0$
$1 \ge 0$ (true, so so we shade above the line)
Red line:
$y\le4$
$1 \le 4$ (true, so so we shade below the line)
Blue line:
$x\ge0$
$1\ge0$ (true, so we shade the right side of the line)
The solution area is the area outlined by the four points in the screenshot.
