Answer
Please see the graph.
Work Step by Step
Orange line: $y+2x\le4$
Green line: $y\le2$
Red line: $y\ge0$
Blue line: $x\ge0$
To determine what sides of the lines to shade, we use a point not on any lines, such as $(1,1)$.
Orange line:
$y+2x\le4$
$1+2*1\le4$
$1+2\le4$
$3\le4$ (true, so we shade the left side of the line)
Green line:
$y\le2$
$1\le2$ (true, so we shade under the line)
Red line:
$y\ge0$
$1\ge0$ (true, so we shade above the line)
Blue line:
$x\ge0$
$1\ge0$ (true, so we shade the right side of the line)
The solution area is the overlap of the four shaded areas--the area bordered by the points $(0,0)$, $(0,2)$, $(1,2)$, and $(2,0)$.
