1. I went back to my hometown yesterday afternoon. -correct
2. I was going back to my hometown yesterday afternoon. — incorrect
3. I was going back to my hometown yesterday in the afternoon. -correct
stephenlearner 2. I was going back to my hometown yesterday afternoon. — incorrect 3.
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stephenlearner2. I was going back to my hometown yesterday afternoon. — incorrect
3. I was going back to my hometown yesterday in the afternoon. -correct
I see no reason why one of these should be deemed incorrect and the other correct. If anything, I would say that (3) seems a bit less likely than (2). In any case, these are not plain, standalone state