how to find the number of subsets? 
Let A = {1, 2, 3, 4, 5, 6, 7, 8} $$S ⊆ P(A)$$ For every subset in S, each
  one contains 4 elements and for every element in A it belongs to 3
  subsets that are in S, how many subsets are in S?

Any ideas how to approach this questions?

The sum of cardinalities of sets in $S$ is $3×8=24$ since each of the $8$ elements in $A$ appears $3$ times. Since each set in $S$ has $4$ elements, $|S|=24/4=6$.
