Java minecraft, especially modded minecraft, can be extremely picky. Some steps I can recommend to try to either get it to run, or to narrow down where the issue lies at.
Install the version of vanilla MC you wish to use and insure it fully loads.
Install the modloader of choice (in your case fabric) and again launch MC and make sure it loads.
Install the mods (or modpack) and again check to see if it fully loads.
If all pass, stop the server, wipe (delete) the world map and start it back up and play.
Common issues with MC not running:
Wrong java version. Latest version of java WILL NOT work with older versions of MC.
MC/modloader version mismaches. Make sure the version of modloader your using matches the version of MC and mods/modpack your using.
Mod conflicts. In the case of modpacks this is rare, but a mod conflict can cause MC to fail to fully load.
Final bit of advice…log files and the console window in AMP can GREATLY help in pinpointing where the loading failed and point you in the direction needed to fix it.
I believe ThePotatoKing is 100% correct here. The screenshot you shared showed some warnings, but nothing that is completely game-breaking because it looks like it is still loading. We can’t tell because its not the compete log file and doesn’t show the point of exactly where its crashing at.
I looked up that modpack, and I am assuming your using Prominence II [RPG] v2.8.4 (the latest version), which that version only supplied the client side modpack and not the server files. The difference here is that some mods, like what ThePotatoKing said, only run client-side.
The last version of that modpack that also supplied the server files was v2.8.0hf. I recommend you download that version of the server files, and then try to figure out what was changed between v2.8.0hf and v2.8.4 and manually update/add/remove mods that were changed between those versions… which will be difficult due to lack, or should I say improper documentation of what was done between those versions, i.e. in the change log it said " * Updated some mods", but doesn’t say which ones so you will need to compare over 300 mods to see what was changed.
In short, either download v2.8.0hf and manually add/update/remove the changed mods to bring that server pack upto v2.8.4, or just stick with v2.8.0hf until they update the modpack with the proper server files.