I have never had this problem before. I have the same Apple I.D. as I've always had. I presume that my username is my full name which appears on my desktop, top right. So I assume that I have two names: (1) my Apple I.D. (used in the App Store) and (2) my user name which is the name that pops up in the Adobe Update box. It asks for my password. I tried proceeding with the Adobe update installation with my username and my correct password in the box. It wiggles and does not allow me to proceed. Next I tried typing in my Apple I.D. and my password and again it wiggles and does not let me proceed. To the best of my knowledge I have only ever had one password and it was updated over the past year as required by Apple. It has always worked before. Where do I go from here?
This is the OS, not Flash Player prompting for the password, as such, it's whatever you use (with admin permissions) to log into your system. see What userid & password do I need to install Flash Player? for more information