Why do I have such a problem when I open someone else's project file, and how to solve it

I'm guessing the problem is that your audio and video have gotten out of sync. One at a time I'd select the audio and the video with the red numbers and right click/link then right click on the red numbers and slip into sync. Hopefully this will sync up the clips.

What's the problem?  Please describe it better.

It looks like some material at the beginning is about 3 1/2 seconds out of sync.  But without watching the edit there's no way to know if that's a mistake or intentional.

Maybe check this:

https://www.youtube.com/watch?v=QNmwI9ACwXI