Thanks, PaulM. The youths are students and it has been earlier mentioned. I think "that-clause" in the sentence is a non-defining clause and so there should be a comma before the clause. Moreover, when-clause and main-clause are not related to each other. Please explain it to me again.
When the four youths went back to their homes that they had left three years before, they became proficient in their respective subjects.
No, the that- clause it is not a non-defining clause, so a comma is not required. "That" cannot possibly be used in non-defining relative clauses; only the wh- relative words can be used.
The when- clause is a supplementary adjunct. It is not tightly integrated into the structure of the clause, but is loosely attached with a comma; in speech it would be marked off by a slight pause. The information the clause supplies is useful, but non-essential. Compare:
(1) The children were playing happily outside. (modifier)
(2) Happily, the children were playing outside. (supplement)
The adverb "happily" is an adjunct in both those examples. In (1) it is of the modifying kind indicating how the children were playing. By contrast, in (2) "happily" is not modifying anything but simply giving the speaker's evaluation of the situation, and hence is a supplement set apart with a comma at the beginning of the sentence.