U = {1,2,3,4,5,6,7,8}
A ={1,3,6,7,8}
B = {1,2,5,6} 
(A' U B')∩ (A U B)'= 

A' = set of all elements in U but not in A = {2,4,5}
B' = set of all elements in U but not in B = {3,4,7,8}
A' U B' = {2,3,4,5,7,8}  ---> (1)

A U B = {1,2,3,5,6,7,8}
(A U B)' = set of all elements in U but not in (A U B) = {4}  --- (2)

So (A' U B')∩ (A U B)'=  {4} which is the only common element between the sets 
as seen from (1) and (2).