I don’t know if this is all that different than what Mike showed by cutting with the “k” key or just moving the selected area to render but I found this way:
I just clicked on the clipped where the left facing triangle is and grabbed and dragged it to frame 270. I then clicked on the end of the clip where the right triangle is and grabbed and dragged it back to the left until it was at frame 390. I then clicked and dragged the clip back to frame 1 so that the selected section was at frame 1 to 120. I rendered that and all worked well. This is the same thing that works in audio editing in my DAW so it was natural to try this approach. I was happy to see that it works in Blender and video editing as well.