uW Translation Notes:

Note 1 topic: figures-of-speech / exclusive

ἡμῖν

˱to˲_us

Here, us refers to Peter and the other apostles whom Jesus chose, not to Cornelius and his guests. So use the exclusive form of “us” if your language marks that distinction.

Note 2 topic: figures-of-speech / explicit

τῷ λαῷ

˱to˲_the people

Connecting Statement:

By the people, Peter means the Jewish people. Alternate translation: [to the Jewish people]

Note 3 topic: figures-of-speech / activepassive

ὁ ὡρισμένος ὑπὸ τοῦ Θεοῦ

the_‹one› ˓having_been˒_designated (Some words not found in SR-GNT: Καί παρήγγειλεν ἡμῖν κηρύξαι τῷ λαῷ καί διαμαρτύρασθαι ὅτι οὗτος ἐστίν ὁ ὡρισμένος ὑπό τοῦ Θεοῦ κριτής ζώντων καί νεκρῶν)

If your language does not use this passive form, you could express the idea in active form or in another way that is natural in your language. Alternate translation: [the one whom God has chosen]

Note 4 topic: figures-of-speech / nominaladj

ζώντων καὶ νεκρῶν

˱of˲_˓the˒_living (Some words not found in SR-GNT: Καί παρήγγειλεν ἡμῖν κηρύξαι τῷ λαῷ καί διαμαρτύρασθαι ὅτι οὗτος ἐστίν ὁ ὡρισμένος ὑπό τοῦ Θεοῦ κριτής ζώντων καί νεκρῶν)

Peter is using the adjectives living and dead as nouns. (The word living is actually a participle, but it functions here as an adjective.) Your language may use adjectives in the same way. If not, you could translate these words with equivalent phrases. Alternate translation: [of those who are alive and of those who have died]