Exegesis:

kagō diatithemai humin … basileian ‘and I assign to you dominion.’ kagō means here ‘I on my part.’ basileian is object of both diatithemai and dietheto and has in both cases the same general and abstract meaning, i.e. ‘dominion,’ ‘royal power.’

diatithemai ‘to ordain,’ ‘to decree,’ ‘to assign.’

kathōs dietheto moi ho patēr mou ‘just as my father assigned (dominion) to me.’

(V. 30) hina esthēte kai pinēte epi tēs trapezēs mou ‘in order that you may eat and drink at my table,’ i.e. that you have fellowship with me at the Messianic banquet, cf. on 5.30. The clause indicates the intended result of the assigning of the royal power to the disciples: they will reign in fellowship with Christ in his kingdom.

en tē basileia mou ‘in my kingdom,’ i.e. ‘when my Messianic kingdom has come.’

kai kathēsesthe epi thronōn ‘and you will sit on thrones,’ syntactically no longer dependent upon hina and describing, together with what follows, the situation in which the royal power will be exercised.

tas dōdeka phulas krinontes tou Israēl ‘judging the twelve tribes of Israel,’ referring to the eschatological judgment. phulē also 2.36.

Translation:

One may have to render v. 29 in two sentences, e.g. ‘my Father appointed a kingdom for me; I on my part appoint (it) for you in the same way,’ or to keep to the clause order of the Greek, e.g. ‘I appoint a kingdom for you in the same way as my Father (on his part) appointed it for me,’ ‘I determine that you receive kingship, just as the Father granted it to me’ (cf. Balinese, where an honorific term for God’s act is required).

My Father, cf. on 2.49.

Appointed a kingdom for me, i.e. caused me to be king/ruler, or, to have royal power/rule/dominion, cf. “made me King” (The Four Gospels – a New Translation), ‘gave me to rule’ (Chol), ‘gave me the right (or, the position) to rule’ (cf. Good News Translation, Otomi).

I appoint for you will require similar adjustments, ‘I cause you to be king,’ etc., or, ‘the same (or, that also) I cause you to be,’ etc.

(V. 30) That you may eat …, or as a new sentence, ‘(so/then) you shall eat….’

Eat and drink at my table, or, ‘eat and drink at-the-same-table (or, from the-same-dish) with me’ (Bahasa Indonesia RC, Malay), and cf. on “eat (and drink) with” in 7.36.

Sit on thrones. For the noun see on 1.32. If a literal rendering is impossible or culturally irrelevant, one may say, ‘to reign in splendour.’

Twelve tribes of Israel, cf. on 2.36; in Huixtec one must say, ‘twelve groups of our (inclus.) people, we who are descendants of (the patriarch) Israel.’

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.