A homeless shelter received donations of 18 mittens and 12 winter hats. What is the greatest number of identical winter clothing sets that they can make, without any leftover mittens or hats?

Each person needs 2 mittens. Since you have 18 mittens (18 / 2) will be the number of of people who get mittens.

Therefore each person will also get 1 winter hat leaving 3 that can be saved for next year.

This problem looks trivial. It is not. Many chemistry problems ask a question such that one chemical is in greater supply than another in a reaction. There is some of one of them left over. Same as the mittens. It's good to think in terms of leftovers.