Part 1
f(g(3))
step 1
Find out g(3)
looking at the graph
For x=3, g(x)=0
so
g(3)=0
Find out f(0)
For x=0, f(x)=2
therefore
f(g(3))=2
Part 2
g(f(2))
step 1
Find out f(2)
For x=2, f(x)=3 ------> f(2)=3
step 2
Find out g(f(2))=g(3)
For x=3, g(x)=0
therefore
g(f(2))=0
Part 3
f(f(4))
step 1
Find out f(4)
For x=4, f(x)=1
step 2
Find out f(f(4))=f(1)
For x=1, f(x)=4
therefore
f(f(4))=4
part 4
g(g(5))
step 1
Find out g(5)
For x=5, g(x)=1
step 2
g(g(5))=g(1)
For x=1, g(x)=3
therefore
g(g(5))=3