Lightroom 6 is not associated with the application manager. The application manager is for use with the creative cloud and with Lightroom CC. So what is it that you really purchased? And where did you download it from?
I bought LightRoom 6 from Adobe. I have the order confirmation and serial
number from the adobe store. I downloaded it from Adobe. It is legit. How
do I get out of the application manager's Catch 22?
It occurs to me to Carolan, I bought the LR6, this morning I have sent in serial number but do not accept it. Help, please!
Select the existing version of LR (the one you are upgrading from) and put in its serial number, i.e. the old serial number. Clunky, and inadequately explained in the setup process.