How many ways are there to put 4 distinguishable balls into 2 indistinguishable boxes?
How many ways are there to split these 4 balls into 2 groups?
Each ball has 2 options, 2^4.
2 groups are interchangable. 2^4/2 = 8.
=^._.^=
This is homework, as are almost all questions, so I will just give you a hint:
the boxes could hold
(0,4) (1,3) or (2,2) balls
You could look at each of these possibilities separately.