Answer
Please see the graph.
Work Step by Step
Green line: $y\ge x$
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.
$y\ge x$
$0\ge 0$ (true)
Since this is true, we shade the side of the line that has the point $(0,0)$.
Red line: $2x-4y\ge6$
$2x-4y\ge6$
$2x-4y+4y-6 \ge 6+4y-6$
$2x-6 \ge 4y$
$(2x-6)/4 \ge 4y/4$
$.5x-1.5 \ge y$
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.
$.5x-1.5 \ge y$
$.5*0-1.5 \ge 0$
$0-1.5 \ge 0$
$-1.5 \ge 0$ (false)
Since this is false, we shade the side of the line that doesn't have the point $(0,0)$.
The intersection of the two lines is the area that is shaded red and green.