F(x,y,z)=F(x’,y,z’) is possible when both XYZ and X'YZ' will be present/absent together in the function.
For example, 000 requires 101(0'00') to be in the function or none should be present in the function. It is analogous to the problem of a couple attending a party. Hence each pair has 2 choices.
Similarly, you will have the following pairs to choose from-
000 --> 101 (0,5)
001 --> 100 (1,4)
010 --> 111 (2,7)
011 --> 110 (3,6)
Now these 4 pairs can be picked in 2^4 ways. Hence 16 functions are possible that satisfy the given constraint.