You mixed up between the two questions.
13. If a - c = b - c, then a = b. This is addition property of equality because you added c to both sides which in turn cancelled the other c yielding a = b.
16. If a + c = b + c, then a = b. This is subtraction property of equality because you subtracted c from both sides to get a = b.
You thought that you should classify the hypothesis as addition or subtraction, but this is not what they asked you for. They wanted you to know which property did you use to come up to the conclusion that a = b. Understand the question completely before attempting to solve it next time.