Possible errors with My Library in the Gallery

SoulHeartGhost​ What I see in your pic is just some of the lots and sims that are in the Library by default out of the box.   Unlike what a player saves to their Library, these are hard coded in the game, and the files do not show up in the Tray folder.  They are always there when a new Tray folder/Library is created.  Some lots are not tagged correctly though even though they show the creator as Maxis.  If you change the filter to Other or All, the rest will show up.

As for the duplicated household, that happens occasionally and you can ignore it usually.  In my game, it comes and goes.  I've never seen it have 6 duplicates though.  The most I've seen is 2 duplicates.  It will clear up on its own in time, but you might be able to fix it sooner by moving the current Tray folder out of The Sims 4 folder to somewhere safe and starting the game.  Just getting to the Main Menu should be far enough, then click on Gallery and click on the Library tab.  Then quit to desktop.  After you quit, delete the new Tray folder that just got created and move your current Tray folder back into The Sims 4 folder. 

Hope this helps.

I tried to remove the Tray folder, but unfortunately the duplicates did not disappear, however, it does not matter. Rather, I still have a question, how many hard coded families should be displayed in the library and if they are missing, why and how to restore them?

SoulHeartGhost​  There are 6.  If they have gone missing, just move your Tray folder to your desktop and start the game.  Once you get to the Main Menu, click Gallery.  Then click the Library tab.  If you look at the Tray folder at that point, it will be empty.  The only way they would go missing is for you to delete them (yes, that is safe to do, same with the default hard coded lots).

Hope this helps.