What is the Folder called Elements 2020 on my system drive

Your catalog will not be deleted and should be found in the Organizer automatically when you reinstall either one of the programs.  (I am assuming that you have not relocated the catalog folder to an unusual place).  Go to Help>System Info in the Organizer and it will tell you the folder location of the catalog.  That folder will contain the file catalog.pse18db.  I suggest you make a copy of that folder as a backup.  The folder only contains the catalog files, not the media files.

If you run into problems uninstalling either Elements programs, you can use the Adobe CC Cleaner tool which also works on Elements.  Note that at one of the first screens listing your installed programs, Elements will not be listed.  But if you select 1. ALL, it will take you to another screen where each of your Elements programs will be listed and can be deleted.

The devil is in the details.  So, the folder you are talking about is actually named Elements 2020 Organizer.

As I mentioned earlier, if you have both PRE and PSE installed and only uninstall one of them, the Organizer folder will remain because the other program still needs it. 

@johnb73471616 said:  In fact there are two sub folders with the same name. One is in folder Program Files and the other in folder Program Files (x86).  They are both on the C: drive.  I suspect the sub folder in Program Files may have been installed when I've been playing with different locations trying to get Premier installed.

The Elements Organizer 2020 folder should NOT be in the Program Files (x86) parent folder. (But that is where your Elements 11 Organizer folder should be.) As you say that you have been playing around with different locations, this is probably the cause of your problems.  My suggestion is that you uninstall both PRE 2020 and PSE 2020 from your computer.  Once you have uninstalled the programs (or even if the uninstall of PRE did not work), move the Program Files (x86)\Elements 2020 Organizer folder to another location.  I would tell you to delete it, but since it is not clear how much playing with locations you have done, I am suggesting to keep it for safety's sake until everything else is up and running.

Reboot your computer and then install the programs again, starting with PSE 2020 and use the default location suggested by the programs. 

There shouldn't be any folder named Elements 2020 on your PC (unless you created one there).   Is that the entire name of what you are seeing?  If so, is the folder on the root of your C drive?  If not, please tell us the entire path to the folder.  Please give us a screenshot of the contents of the folder. 

And without knowing more, let me just say that if you have both Photoshop Elements and Premiere Elements installed, they both use the Organizer.  So, if you uninstall one of the editing programs, the Organizer will not be deleted.

Elements 2020 is the editor.  Premier Elements edits videos.  When you have problems installing / reinstalling it typically is due to "parts" of the program still running in the background, even though you have closed it, it just happens sometimes. 
View background processes as mini programs that do specific things.

There is more than one folder labelled "elements 2020" (or any other version) on your computer. 

There really is no reason for the average user to be concerned with the processes you see listed below.  I have 4 or 5 adobe things open right now, that's why you see many Adobe things open.



I often used cCleaner to uninstall things, other use other utilities, I also just use the uninstall feature built into windows.  Use  whatever makes you happy.

HOW TO FIX IT SO YOU CAN INSTALL IT:

Turn your computer all the way off.
Go get a cup of coffee.
Turn your computer back on.
Begin the installation of Premier Elements.     I usually just redownload it from my adobe account.   You can use a disc if you want-