To visually determine the solution for the compound inequality $x > -3$ and $x \leq 2$, graph each inequality on a number line and locate the intersection. The graph of $x > -3$ extends to the right of $-3$ (not including $-3$), while the graph of $x \leq 2$ extends to the left of $2$ (including $2$). The overlapping region—where numbers are shaded on both individual graphs—forms the solution. Because $-3$ is not shaded on the first graph, it is excluded from the solution. The number $2$ is shaded on both, so it is included. The final solution spans the interval strictly between $-3$ and up to and including $2$.