MartianRoleplay did you edit the Apache configuration to set the public_html/public folder as DocumentRoot?
Next you should check rewrites are enabled and the htaccess file is actually picked up by the webserver.
If that's still not working, it might be related to file permissions. Check which user should own the files and change it from ftp to (on some hostings) www-data. If your hosting does not let you change file ownership, you might need to change file permissions, althought what I'm seeing in the screenshot should at least let you access the forum without error.
