Answer
a) $4$
b) $3$
c) $0$
d) $Undefined$. See below.
e) $4$
f) $-2$
Work Step by Step
a) $f(g(2))=f(5)=4$
b) $g(f(0))=g(0)=3$
c) $f(g(0))=f(3)=0$
d) $g(f(6))=g(6)= undefined$ because it does not exist on the graph.
e) $g(g(-2))=g(1)=4$
f) $f(f(4))=f(2)=-2$