Exegesis:

kai ean ekei ē huios eirēnēs lit. ‘and if there is a son of peace there.’ Here ‘son of peace’ means a person who is destined to have/receive peace, cf. Strack-Billerbeck II, 166.

epanapaēsetai ep’ auton hē eirēnē humōn ‘your peace will rest upon him.’

epanapauomai ‘to rest (upon)’ is used in Num. 11.25f of the spirit that rested upon the seventy elders (cf. also 2 Kings 2.15). The picture is here that of a blessing, as it were released by the speaking of the word eirēnē (hence hē eirēnē humōn ‘your peace’) and subsisting apart from that word.

ei de mēge, scil. ē huios eirēnēs ekei ‘if (there is) not (a son of peace there).’

eph’ humas anakampsei ‘it will (turn around and) come back to you.’ anakamptō.

Translation:

A son of peace. The phrase may be rendered, ‘one who can (or, is ready to) receive peace,’ ‘one who has an expectation of peace’ (Sinhala), ‘a man who is worthy of (or, to receive) peace’ (cf. Bahasa Indonesia 1968). It is essential that both here and in the next clause the relationship with ‘peace’ in v. 5 be preserved in translation.

Your peace, i.e. the peace you have wished; hence, ‘your greeting of peace’ (Kituba), ‘your saying of being-well’ (Balinese), ‘that prayer of you’ (Tae’ 1933), ‘the blessing you ask for him’ (Tzeltal).

Rest upon him, or, ‘stay with him,’ ‘bless him.’ Descriptive or idiomatic terms or phrases for ‘peace’ may influence the rendering of this clause, e.g. ‘your wish of well-being will make him well.’

Return to you, or, “return and rest upon you” (New English Bible), ‘come to rest upon you again,’ or further shifts in accordance with those in the preceding clause.

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.