Answer is (D).
$f(x,y,z) = f(x', y',z')$, means output should be same for $(0,0,0)$ and $(1,1,1)$, $(0,0,1)$ and $(1,1,0)$, $(0,1,0)$ and $(1,0,1)$, $(0,1,1)$ and $(1,0,0)$ and the other input combinations repeat after this.
So, We have four input cases (pairs) for which output can be $0$ or $1$. So, we have two cases for each pair.
Total functions possible $= 2*2*2*2 = 16$