Excuse me, but I get this error after I enter "sudo apt-get install ffmpeg obs-studio" into the terminal. I was wondering what the problem is and how I can fix it if there is a way to currently fix it. Thank you.
Either you are not running 14.04 or something is wrong in your distribution name. If you look at the error output, it says it is searching for a Saucy (13.10) package, but there are only Trusty (14.04) packages in that PPA.
You need to edit the btbn*.list file in /etc/apt/sources.list.d/ and replace saucy with trusty. But before you do that, you really should check if you are actually running Ubuntu 14.04!