Subsets having AT MOST 4 elements, means the subsets could have:
4 elements (at most)
3 elements
2 elements
1 element
0 element (nil element = Ф)
You can solve through combination; However remember that
ⁿCₓ = (n!)/(x!)(n-x)!
4 elements = ⁸C₄ = 70
3 elements = ⁸C₃ = 56
2 elements = ⁸C₂ = 28
1 element = ⁸C₁ = 8
Ф element = ⁸C₀ = 1
Adding up gives 163 subsets with at most 4 elements