Exegesis:

kai egeneto ‘and it happened,’ cf. on 1.8, introduces an independent narrative without connexion with the preceding as to time and place.

en tō einai auton proseuchomenon kata monas lit. ‘during his praying alone,’ hence ‘when he was praying alone.’ kata monas does not exclude the presence of the disciples as shown by what follows.

sunēsan autō hoi mathētai ‘his disciples were with him,’ connecting clause after kai egeneto, best understood as implying that the disciples did not take part in the praying.

suneimi with following dative ‘to be with (somebody).’

kai epērōtēsen autous ‘and he asked them.’ Here begins the narrative proper. For eperōtaō cf. on 2.46.

tina me legousin hoi ochloi einai? ‘who do the people say that I am?’ hoi ochloi is not to be understood as taking up hoi ochloi in v. 11 and later references (vv. 12, 13, 16); hence a general rendering like ‘the people’ is preferable.

Translation:

The introductory sentence may have to be adjusted, e.g. ‘once he/Jesus was praying alone and the/his disciples were with him (or, were near him/nearby, or, were there also, or, were at the same place).’

Alone, or, “by himself” (An American Translation), “in retirement” (The Four Gospels – a New Translation, which may lead to a further shift ‘once Jesus had retired (from the crowd) for prayer…’).

Who do the people say that I am, see ‘in the opinion of the people/crowd, who am I said (to be)’ (cf. Balinese, Javanese).

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.