In this passage, scribe 2 of 𝓟 did not write the definite article the before the second occurrence of people; Oliver Cowdery supplied it when he proofed 𝓟 against 𝓞. There are many examples in the printer’s manuscript where scribe 2 initially omitted the definite article the or it was supplied later by Oliver when he proofed 𝓟 (see the list under Alma 2:4), so one could presume here that the the was originally in 𝓞 and scribe 2 omitted it. On the other hand, it is possible that Oliver’s addition of the was due to conscious editing on his part since there is the preceding sentence in this passage that refers to Alma’s teaching of the people in Melek: “and he began to teach the people in the land of Melek”. In other words, one could argue that the virtual identity of that sentence with the following “and he began to teach people throughout all the land of Melek” led Oliver to emend that instance of “teach people” to “teach the people”; it’s even possible that the change occurred accidentally, with Oliver’s eye straying back two lines in 𝓞 as he proofed 𝓟 against 𝓞.
In almost all instances, the word people in the Book of Mormon text is preceded by a determiner of some kind (like the, a, his, this, all, and so forth). There are only a few examples where people is used in a nondeterminative or partitive sense (none of which refer to teaching people):
In addition, there is one passage where Oliver Cowdery himself twice omitted the definite article the before people, initially when he took down Joseph Smith’s dictation and permanently when he copied the text from 𝓞 into 𝓟:
See under Alma 32:2 for additional discussion of this example (which also involves the replacement of poorer with poor when Oliver copied the text into 𝓟). This example shows that there was a minor tendency on Oliver’s part to replace determinative uses of people with partitive ones.
In any event, the original reading in 𝓟 for Alma 8:4 (namely, “he began to teach people throughout all the land of Melek”) is theoretically possible. Yet elsewhere when the verb is teach, the text consistently prefers “teach the people” over “teach people” when there is a choice, as in the following list (where I include the first example of “teach the people” in Alma 8:4, for which the text is firm):
Overall, the evidence indicates that the original text for Alma 8:4 probably read with the definite article the in both instances: “and he began to teach the people in the land of Melek … and he began to teach the people throughout all the land of Melek”.
Summary: Accept in Alma 8:4 Oliver Cowdery’s inserted the as the reading of the original text; the definite article is expected before people in this context; in addition, there is considerable evidence that scribe 2 of 𝓟 frequently omitted the definite article.