Exegesis:

tote arxesthe legein lit. ‘then you will begin to say.’ tote ‘then,’ i.e. when the master of the house has denied the relationship (v. 25). arxesthe indicates that the activity of those whom Jesus addresses takes a new turn in that they attempt to prove their relationship to the householder, cf. on 4.21.

ephagomen enōpion sou kai epiomen ‘we ate and drank in your presence,’ i.e. ‘we had fellowship with you at table,’ cf. on 5.30. enōpion sou goes with both verbs which form one expression. For enōpion cf. on 1.15.

en tais plateiais hēmōn edidaxas ‘you taught in our streets,’ i.e. in the streets of the towns in which we live, implicit reference to Jesus’ activity as a teacher.

Translation:

We ate and drank in your presence, preferably, ‘with you’; or, ‘we sat at table (or, had meals) with you’ (cf. New English Bible, Phillips); and cf. the note on 5.30.

In our streets, or, ‘in the roads/paths/trails of our towns and villages,’ ‘in our village-squares’ (cf. Kele, one West Nyanja version), ‘on the crossroads of our villages,’ or simply, ‘in our settlements’ (Tae’); cf. on 10.10.

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.