[algebra, factoring polynomials] Anyone experienced with math please help!!

So I followed along with a video my teacher sent, and I did the method accordingly. However, on the next page, there was the built-in online school video, which showed me a different method. I wanted to try solving it on my own so I did the teacher's method, but when I got the answer revealed I was off quite a bit. Could someone explain why my method didn't work?

The first picture, albeit crossed out, was what I did. What's written on the right of the first pic were just notes taken from the built-in video. The second was what was shown in the built-in video written down. The third picture is an example question of what my teacher taught me for reference, and the last one is the built-in video explanation. I'd really appreciate the help