Hello Hribich,
Welcome to Apple Support Communities.
We understand that you are not able to see the person on your FaceTime video. We are happy to help.
The article that brought you to us, If FaceTime isn't working on your Mac - Apple Support, may have resolved this with the steps in the section titled “If your camera or microphone doesn’t work”.
Have you made any changes to your Mac? If so, what changes have you made? What is the exact error message you receive, if any?
We’d like to have you test in safe mode to isolate the cause. Here’s how to use safe mode: How to use safe mode on your Mac - Apple Support
"Apple silicon
- Shut down your Mac.
- Turn on your Mac and continue to press and hold the power button until you see the startup options window.
- Select your startup disk, then press and hold the Shift key while clicking “Continue in Safe Mode.”
- Log in to your Mac. You might be asked to log in again.
Intel processor
- Turn on or restart your Mac, then immediately press and hold the Shift key as your Mac starts up.
- Release the key when you see the login window, then log in to your Mac.
- You might be asked to log in again. On either the first or second login window, you should see ”Safe Boot” in the upper-right corner of the window."
Let us know if you have further questions.
Take care.