This Maxim is an interesting one in that it does not tell us for whom we should be fulfilling favors. Are we to fulfill what we tell someone we will do for them? Of course we should. Are we to do favors for others? Again, of course we should. Are we to be thankful for the favors that others have done for us and return them if possible? For a third time, of course we should. Which of these things is it that the ancients were referring to? Possibly all of the above is my answer.
We should always fulfill the favors we owe to others as well as the ones we promise others that we will do for them. This is basic courtesy as well as being a simple interpretation of this Maxim. In this case, the simple interpretation is likely the best one. As humans our society is built on the doing of favors for one another and the fulfilling of the obligations those favors create. This makes this perhaps one of the most important yet less well known of the Maxims.