Answer: As i understand, the set is P = {a,b,c,d}
then all the proper subsets are all the sets that belongs to P, that are different of P. Then A is a subset of P if all the elements of A belongs to P, but A is not equal to P
this is:
the sets of one element : {a}, {b}, {c}, {d} and the null set; ∅
sets of two elements: {a,b} , {a,c} , {a.d}, {b,c}, {b,d}, {c,d}
sets of three elements : {a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}
and there arent sets of 4 elements or more.