Answer
The solutions of the equation $f(g(x))=0$ are $$x \approx 1.5$$ $$x \approx -1.5 \, .$$
The solutions of the equation $g(f(x))=0$ are $$x \approx -2$$ $$x \approx 2 \, .$$
Work Step by Step
According to the graphs of $f$ and $g$, since $f(x)=0$ for $x \approx -2, x \approx 2 $, the solutions of $f(g(x))=0$ are $x$ for which $g(x) \approx -2$ or $g(x) \approx 2$, that is, $$x \approx 1.5 \quad g(1.5) \approx -2,$$ $$x \approx -1.5 \quad g(-1.5) \approx 2.$$
According to the graphs of $f$ and $g$, since $g(x)=0$ for $x \approx 0$, the solutions of $g(f(x))=0$ are $x$ for which $f(x) \approx 0$, that is, $$x \approx -2 \quad f(-2) \approx 0,$$ $$x \approx 2 \quad f(2) \approx 0.$$
