The subsets of {10, 19, 5, 0} are
{ } - the empty set, or 1 subset of size 0
{10}, {19}, {5}, {0} - 4 subsets of size 1
{10, 19}, {10, 5}, {10, 0}, {19, 5}, {19, 0}, {5, 0} - 6 subsets of size 2
{10, 19, 5}, {10, 19, 0}, {10, 5, 0}, {19, 5, 0} - 4 subsets of size 3
{10, 19, 5, 0} - 1 subset of size 4
A proper subset of a set is any subset of that set that is not equal to that set. The only subset that is not a proper subset is {10, 19, 5, 0}, since that's the set itself. So there are 15 proper subsets.
In general, a set of size n has a total of 2ⁿ subsets, and 2ⁿ - 1 proper subsets.