The excerpt of this badge says: Edited first post that was inactive for 6 months.
But I am a member for just 3 months.
Don't I understand the badge explanation?
It doesn't have to be your own post. You could have edited someone else's post that was 6 months old.
Your SO profile links to information about the badge you've earned, showing that the question for which you earned this badge is this one: Lesser known language constructs of Object Pascal (Delphi).