Exegesis:
kai autos edidasken ‘and he taught,’ iterative imperfect. kai autos ‘and he’ unemphatic as in 1.17.
didaskō ‘to teach,’ in Luke always of the teaching of Jesus.
en tais sunagōgais autōn ‘in their synagogues.’ autōn refers by inference to the inhabitants of Galilee.
sunagōgē lit. ‘the bringing together’ (from sunagō ‘to gather’), hence the place where people are brought together, has become the technical word for the local place for worship, religious teaching and for the administration of justice among the Jews. For a detailed account cf. IDB IV, 476-491.
doxazomenos hupo pantōn ‘being glorified by all,’ participial phrase describing the result of Jesus’ teaching in the synagogues. For doxazō cf. on 2.20.
Translation:
He taught. For the verb ‘to teach’ (also in 4.31f; 5.3, 17; 6.6, 40; 10.39; 11.1; 12.12; 13.10, 22, 26; 19.47; 20.1, 21; 21.37; 23.5, and cf. on “teacher” in 2.46). It may be obligatory to add a reference to those taught, e.g. ‘the people (there),’ or to the thing taught, e.g. ‘the way of God’ (cf. 20.21). Elsewhere ‘to teach’ is rendered by a causative form of ‘to learn’; and in some languages (e.g. Dutch, Ekari) one verbal form is used for both activities, which may make necessary the addition of an object to avoid ambiguity, compare ‘those who learn/teach people’ for ‘teachers’ with ‘those who learn/teach’ for ‘disciples’ (Ekari). In Auca, where the concept is expressed by juxtaposing ‘to speak’ and ‘to hear’ in a cause-result relationship, ‘he teaches’ must be rendered by ‘he speaks (that they may) hear.’ In many Indonesian languages the common word for ‘teacher’ (guru, originally a borrowing from India) can have a religious connotation which the (non-cognate) verb ‘to teach’ has not, or has less clearly; hence, to indicate religious teaching a derivation of the former term may be preferable, e.g. ‘to act-as-guru’ (Tae’).
Their synagogues, or, ‘the synagogues of the people there’ (cf. Javanese), or shifting to a locative qualification, ‘the synagogues there’ (cf. Balinese). For synagogue (also in 4.20, 28, 44; 6.6; 7.5; 8.41; 11.43; 13.10, 14; 20.46; and, referring not to the place but to the congregation in it, 12.11; 21.12) cf. ‘place to talk God’s talk’ (Wantoat), ‘house where God is remembered’ (Tabasco Chontal). The rendering ‘place-of-teaching’ will do only where ‘to teach’ clearly refers to religious education. Some Indonesian languages use their term for ‘mosque,’ or for a Muslim building/institution of a less official type; in some cases, however, such a rendering has been replaced in revision by a term or descriptive phrase with a less strongly Muslim connotation, e.g. ‘house of prayer’ (Bahasa Indonesia).
Being glorified by all, or, ‘and/so that all people praised/honoured him,’ ‘all-of-them very good what they said about him’ (Tzeltal). For to glorify see on 2.20.
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.