Answer
Please see the graph.
Work Step by Step
Orange line: $x^{2}+y^{2}\le16$
Red line: $x^{2}+y^{2}\geq4$
To determine what sides of the lines to shade, we pick the point $(0,0)$ and determine if the inequalities are valid. We will use a solid orange line and a solid red line since the two inequalities respectively have a less than or equal to sign and a greater than or equal to sign.
$(0,0)$
$x^{2}+y^{2}\le16$
$0^{2}+0^{2}\le16$
$0 +0 \le 16$
$0 \le 16$ (true, so we shade inside the circle)
$(0,0)$
$x^{2}+y^{2}\geq4$
$0^{2}+0^{2}\geq4$
$0 + 0 \geq 4$
$0 \geq 4$ (false, so we shade outside the circle)
The overlap of the two graphs is the solution set for the set of inequalities.
