TITLE: How is this problem called?
QUESTION [5 upvotes]: I have a set of integers $\{8, 8, 6\}$. I want to know if It is possible to get $21$ by adding a subset of them. I would like to know how is the problem called so that I can google it.

REPLY [2 votes]: This "set" is an example of what is sometimes called a "multiset": it allows one member (in this case 8) to have multiple memberships in it rather than only one.
You can't get an odd number such as 21 by adding even numbers.