Answer
Please see the graph.
Work Step by Step
Green line: $2x+y>4$
$2x+y-2x>4-2x$
$y > 4-2x$
Since we have the "greater than" sign, we use a dotted line. Let's use the point $(0,0)$ to see what side of the line we shade.
$y\gt 4-2x$
$0\gt 4-2*0$
$0\gt 4-0$
$0\gt 4$ (false)
Since this is false, we shade the side of the line that doesn't have the point $(0,0)$.
Red line: $x\ge1$
Since we have the "greater than or equal to" sign, we use a solid line. Let's use the point $(0,0)$ to see what side of the line we shade.
$x\ge1$
$0 \ge 1$ (false)
Since this is false, we shade the side of the line that doesn't have the point $(0,0)$.
The union of the two lines is the area that is shaded red or green.