Can’t seem to find the option underneath the Vertex tab in 2.93 LTS:
Using Alt+M did something else entirely–earlier I selected the top 4 vertices and hit Alt+M and it disconnected those vertices from the other edges so when I move each point or the whole face it was as if it was detached from the rest (the option was called Split instead).
Later versions of Blender than the one used in the course changed ‘Remove Doubles’ to ‘Merge by distance’. This can be accessed by the shortcut M and Select the merge type you want. (For a time it was Ctrl M) It will depend on the version you are using. Or f3 and search Merge.
Plain M is the current release and seems settled there now!