i.e., from what parts of the Earth would it have been possible to directly listen to the broadcast with
a shortwave an amateur radio receiver?
On a related note, which of NASA's tracking stations were in view?
The reading began at 03 14 06 56 of the mission, which is to say, 3 days, 14 hours, and almost 7 minutes after launch. They launched at 12:51 UTC on Dec 21, 1968 (just before 8 a.m. at Cape Canaveral). So, doing the conversion, that was 2 minutes before 10 p.m. on the east coast of the US, and just before 7 p.m. on the west coast.
According to this Day and Night World Map of that moment, the Moon was directly over Hawaii.
With the proper equipment, someone in the Americas or on the Pacific Rim could have listened in.
The other answers show in more visible terms but there is a more direct way of seeing who could have heard it.
Remember that radio and light are both electromagnetic waves and we have a direct picture of where light would be visible.
OK not exactly when the verse was given. I wrote this based on my memory and thought this was taken at the exact time but it was worth getting this photo in :)