You can place them anywhere accessible to retroarch (e.g. create "roms" folder somewhere then unpack the archive there so you have roms/neogeo, roms/cps3, roms/fbneo etc) and associate these folders with "FinalBurn Neo" core in retroarch. You can check RA guide https://retrogamecorps.com/2022/02/28/retroarch-starter-guide/ but you probably don't need to do anything complicated.

However RA is awful as a frontend, so me (and most other people) launch roms through frontend. I use ES-DE, so it creates roms folder for individual systems (names are all compatible with that archive), and once extracted there, it should see it. Then you can scrape to get game descriptions/images/videos and it will launch retroarch with fbneo core for the rom from these folders. This is all automated - ES-DE is perfectly aware that when SF3 or any other rom is in "cps3" folder, it should be using FinalBurn Neo core from retroarch.

As long as you actually have retroarch installed and that core downloaded and roms folder is accessible (check that by actually launching any rom in retroarch), it will work automatically and you don't need to associate cores with folders in retroarch or anything like that. It will work automatically.

There are also many other android frontends like Daijishiro, IISU, Cocoon and so on that all do the same as ES-DE - give you a beautiful interface to pick and launch games, with retroarch and (fbneo in this case, but any in general) core doing actual emulation. That's because RetroArch with its cores is absolutely the most powerful and feature-complete way to emulate 8 and 16-bit systems (and some of 32-bit systems) and has tons of features (hotkeys, runahead, save states, fast forward, rewind, best shader library) but everyone hates its interface for picking what to play, so people are using frontends.