Exegesis:

kai egeneto … heuron auton ‘and it happened that they found him’; here it indicates that the climax of the story is at hand: they found him, of all places, in the temple.

meta hēmeras treis ‘after three days,’ i.e. most probably on the second day after the day of their departure from Jerusalem, because according to Jewish and Greco-Roman time-reckoning the day of departure is counted as a full day.

en tō hierō ‘in the temple,’ to be taken with heuron auton ‘they found him.’

kathezomenon en mesō tōn didaskalōn ‘sitting among the teachers.’ For the correct interpretation of this phrase two considerations are important: (a) public teaching in the temple was customary, especially at the occasion of the great festivals and discussion between teachers and questions from the listeners were an essential part in Jewish teaching methods (cf. Strack-Billerbeck II, 150); hence there is nothing out of the ordinary in the scene in the temple and there is no reason to imagine Jesus as teaching the teachers; (b) en mesō, preferably rendered as “surrounded by” (New English Bible), cf. 8.7; 10.3; 22.27, 55; 24.36, is best understood from the point of view of Joseph and Mary, not of the teachers: for the parents who have been looking for him for two or three days, Jesus is in the centre of the scene. kathezomai.

kai akouonta autōn kai eperōtōnta autous ‘and listening to them and asking them questions.’ The first and the second kai are different in function, because akouonta ‘listening’ and eperōtōnta ‘asking questions’ belong together closely, as contrasted with the preceding kathezomenon ‘sitting,’ and express together what Jesus was doing while sitting.

eperōtaō ‘to ask a question’ with the accusative of the person to whom the question is addressed. Sometimes it is used of the asking of questions in discussions, cf. 6.9; 20.21, 27; see also on next verse.

Translation:

After three days. The idiomatic way to indicate the intended time limit often will be different (cf. on “eight” in 1.59); in English, for instance, one normally would say, “two days later”, “the day after the next”, in Balinese, ‘on its after to-morrow.’ It is preferable to use such an idiomatic rendering. (For a probably necessary exception see on 9.22, “on the third day be raised”.)

Sitting, or, ‘where he sat,’ ‘as he was sitting’; or co-ordinated, ‘There he sat.’ — To sit. In some languages usage makes preferable a more generic rendering, e.g. ‘to be,’ ‘to be present,’ ‘to stay,’ or even omission of any verb (‘found him among the teachers’), whereas in others it tends to be more specific, e.g. ‘to sit-cross-legged,’ ‘to sit-with-the-legs-at-the-side-of-the-body.’ The generic rendering is acceptable because it is not Jesus’ act of sitting but the place where he was found that counts in the narrative; the specific rendering is acceptable provided that the term chosen fits the situation as envisaged according to local custom.

Teacher (also in 5.17; 6.40; 8.49; 22.11; and as polite form of address, cf. on 3.12). The rendering often is a phrase built on the verb ‘to teach’ (for which cf. below on 4.15), e.g. ‘those who habitually/professionally teach,’ ‘those who always taught there’ (Tboli), or an agent noun of that verb; sometimes a specific noun exists, e.g. ‘guru’ (in some Indic and Indonesian languages). The term usually has a connotation of status, hence The Four Gospels – a New Translation‘s “Doctors”.

Listening to them and asking them questions. The two participles form a closely connected pair here, which may be indicated by the use of a stronger connective, e.g. ‘and also,’ ‘as well as,’ or by only once naming the object, if the syntactic structure of the receptor language allows doing so. For to listen cf. on “heard” in 1.41. Asking them questions. The aspect is iterative, as expressed by the plural form of the noun in English (cf. also ‘many-things also he asked,’ Tae’ 1933), by reduplication in several Indonesian languages. That the phrase implies discussion may lead to the use of such expressions as, ‘to question-answer’ (Bahasa Indonesia) and ‘in-turns taking-up speech’ (Balinese).

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.