Answer
Please see the graph.
Work Step by Step
Red line: $y\gt 2x+3$
Blue line: $x\le-3$
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Red line: $y\gt 2x+3$
$y\gt 2x+3$
$0 \gt 2*0+3$
$0 \gt 0+3$
$0 \gt 3$ (false)
We'll shade the side of the red line that doesn't have $(0,0)$ on that side. We have a "greater than" sign, so we'll use a dotted line.
Blue line: $x\le-3$
$x \le -3$
$0 \le -3$ (false)
We'll shade the side of the blue line that doesn't have $(0,0)$ on that side. We have a "less than or equal to" sign, so we'll use a solid line.
The union of the two areas is the area that is shaded blue and red.