libraries/fof (f oh f) is part of Joomla 3. It's a really old version of FOF 2 that's been end of life since June 2016. Do not delete, your site will break.
libraries/f0f (f zero f) is an old version of FOF 2 we had to create when Joomla started including FOF in it but forbade us from providing updates or overwriting it with updated versions. We have not been using it since May 2015. However, third party extensions may be using it. Keep a copy of this folder and try to uninstall the F0F extension from your site's backend and see if anything breaks. If it does, restore the folder from your copy.
libraries/fof3 is the previous version of FOF, FOF 3.x. We no longer use it as of March 2nd, 2021. Third party extensions might be using it. Like above, keep a copy of this folder and try to uninstall the FOF 3.x file extension from your site. If it refuses to uninstall you need to keep it. If it uninstalls and something breaks restore the folder from your copy.
libraries/fof4 is the current version of FOF, FOF 4.x. We use it in our software starting March 2nd, 2021. Do not remove it.
Finally note that FOF 3 is deprecated and will become end of life on December 31st, 2021. At this point in time we will issue a final update which will automatically uninstall FOF 3 from your site, the same way that the final update to Adobe Flash uninstalled it.
We are working on future versions of Akeeba Backup and Admin Tools which will no longer rely on FOF at all. The caveat is that they can only work with Joomla 4 since Joomla 3 is missing a lot of the core framework features we need (web assets manager and namespace support being the top reasons).
Nicholas K. Dionysopoulos
Lead Developer and Director
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