How do I delete a catalog from Photoshop elements 2020?

It's very easy to delete a catalog in the organizer, but you should reconsider your option to split catalogs.

1 - delete a catalog: in the catalog manager, open another existing catalog (create a new empty one if necessary). The catalog manager shows a button 'remove' which will delete any catalog except the currently used one. Alternatively, find the location of the catalog folder, menu Help >> System Information. You can use your Explorer to delete the folder when the organizer is not in use.

2 - Splitting or merging catalogs: that's practically impossible to do easily with the organizer and a bit tricky with other catalog-based asset managers like Lightroom.

https://johnrellis.com/psedbtool/photoshop-elements-faq.htm#_Splitting_and_rearranging

3 - Unless your goal is to make sure that there is absolutely nothing in common in two catalogs, the easiest choice is to keep a single catalog. Splitting catalogs in the hope of faster workflow is inefficient and brings many big issues including the near impossibility to merge catalogs afterwards. Simply use keywords to differentiate your themes (or/and adjust your media folder trees)

Go to the File>Manage Catalogs dialog.  If you have more than one catalog available, open one that you want to keep.  You can then select the one that you want to delete and click the Remove button.  A warning will appear asking you if you are sure you want to delete it.  If you only have one catalog, you will need to create and open a new (even empty) catalog in order to delete the existing catalog. 

Alternatively, you can simply delete the catalog folder using Windows Explorer.  The location of the current catalog can be found by using the Help>System Info menu choice.

But why do you want to use more than one catalog?  It is not a recommended approach. There are many ways to filter a catalog to find what you are looking for.