Enter the app. In the main menu, in the list on the left, select "Shows." Now, select "Search." In the search bar, type in "Sonic." The show "Sonic For Hire" should appear. Select it. Select season 6 in the "Seasons" list and episode 10 in the "Episodes" list. The video is called "Sonic For Hire Season 7 Trailer." At 38 seconds long, it is one of the shortest videos in the app. Once the video has ended, simply press the A button to start the video again.
While playing the video, press the A button to show the video controls and select the star symbol on the right to "favorite" the video. This enables you to access the video from the app's main menu in the "Favorites" tab.
To see the exact number of videos you have watched, go to the Xbox One dashboard, highlight the Machinima app, and press the menu button on the controller. Select "View app details" from the list. Now scroll to the right to see the "Videos Watched" leaderboard.
Alternatively, you can simply select any video you want, fast forward it until there are only a few seconds left, and then resume play at normal speed. Fast forwarding through the entire video doesn't count. However, I find that this method requires too much attention. I prefer the Sonic For Hire method, in that once you hear the video stop, you just simply have to press A to start the video again.