Answer
Please see the graph.
Work Step by Step
Green line: $x+y\le0$
Since we have the "less 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.
$x+y\le0$
$x+y\le0$
$0 \le 0$ (true)
Since this is true, we shade the side of the line that has the point $(0,0)$.
Red line: $3x-6y\ge12$
$3x-6y\ge12$
$3x-6y+6y-12\ge12+6y-12$
$3x-12\ge6y$
$(3x-12)/6\ge6y/6$
$.5x-2 \ge y$
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.
$.5x-2 \ge y$
$.5*0-2 \ge 0$
$0-2 \ge 0$
$-2 \ge 0$ (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.