Answer
$f(g(2))=2$
$g(f(-2)=-2$
Work Step by Step
We know that $g(2)=-2$ and $f(2)=f(-2)$ (because f is even):
$f(g(2)=f(-2))=f(2)=2$
$g(f(-2)=g(f(2))=g(2)=-2$
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