Exegesis:

tou dounai gnōsin sōtērias tō laō autou ‘to give knowledge of salvation to his people,’ either explains hetoimasai, or is parallel with it, preferably the former.

gnōsis (also 11.52) ‘knowledge,’ always with a religious connotation.

sōtēria ‘salvation,’ here in a religious sense as the subsequent clause shows.

en aphesei hamartiōn autōn ‘in the forgiveness of their sins’; autōn refers to the individual members of the laos ‘people.’ The phrase goes either with dounai gnōsin sōtērias or with sōtērias only, preferably the latter; this means that salvation consists in the forgiveness of sins.

aphesis ‘release from captivity’ (4.18), ‘remission of debt,’ hence ‘forgiveness’ in the sense of ‘the act of forgiving.’

hamartia ‘sin,’ in the plural ‘sinful actions’; in Luke hamartia occurs always in connexion with forgiveness or forgiving and hence refers to the guilt of sin.

Translation:

To give knowledge of salvation to his people. One or both of the verbal nouns may have to be changed into a verb, e.g. ‘to make known to his people salvation,’ ‘to cause his people to know that they are saved’; or in the active voice with appropriate adjustments ‘to cause his people to know (or, to tell his people) that the Lord saves them.’ For his people, i.e. ‘the Lord’s people,’ ‘the people the Lord rules,’ cf. above on v. 68.

In the forgiveness of their sins. The preposition serves here to introduce that in which salvation consists, that which is the contents of salvation. This can often be expressed by equating ‘salvation’ and ‘forgiveness’; hence, ‘(that is,) forgiveness…,’ ‘which is forgiveness…’ (Tagalog); or, using a verbal clause, ‘that their sins are forgiven’ (Balinese), ‘that is, he has forgiven them their sins’ (Kituba). Idiom may require minor syntactic shifts without appreciable difference of meaning, e.g. ‘to forgive a person’s sins,’ ‘to forgive a person who has sinned,’ ‘to forgive (his) sins to a person,’ ‘to forgive a person as to (his) sins.’ The verb occurs also in 7.42f, in the sense of ‘to cancel debts,’ and in 6.37 (for Gr. apoluō) with a juridical connotation ‘to acquit/to set free.’

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.