Him (touton). “This one,” resumptive and emphatic object of “did crucify and slay.”
Being delivered up (ekdoton). Verbal adjective from ekdidōmi, to give out or over. Old word, but here only in the N.T. Delivered up by Judas, Peter means.
By the determinate counsel and foreknowledge of God (tēi hōrismenēi boulēi kai prognōsēi tou theou). Instrumental case. Note both purpose (boulē) and foreknowledge (prognōsis) of God and “determined” (hōrismenē, perfect passive participle, state of completion). God had willed the death of Jesus (Joh 3:16) and the death of Judas (Act 1:16), but that fact did not absolve Judas from his responsibility and guilt (Luk 22:22). He acted as a free moral agent.
By the hand (dia cheiros). Luke is fond of these figures (hand, face, etc.) very much like the Hebrew though the vernacular of all languages uses them.
Lawless men (anomōn). Men without law, who recognize no law for their conduct, like men in high and low stations today who defy the laws of God and man. Old word, very common in the lxx.
Ye did crucify (prospēxantes). First aorist active participle of prospēgnumi, rare compound word in Dio Cassius and here only in the N.T. One must supply tōi staurōi and so it means “fastened to the cross,” a graphic picture like Paul’s “nailed to the cross” (prosēlōsas tōi staurōi) in Col 2:14.
Did slay (aneilate). Second aorist active indicative with first aorist vowel a instead of o as is common in the Koiné. This verb anaireō, to take up, is often used for kill as in Act 12:2. Note Peter’s boldness now under the power of the Holy Spirit. He charges the people to their faces with the death of Christ.