Albert Barnes on Acts 13:39

And by him. By means of him; by his sufferings and death.

All that believe. Mk 16:16.

Are justified. Are regarded and treated as if they were righteous. They are pardoned, and admitted to the favour of God, and treated as pardoned sinners, and as if they had not offended. See this point explained in Rom 1:17; Rom 3:24, Rom 3:25; Rom 4:1, and Rom 4:2-8.

From all things. From the guilt of all offences. All will be pardoned.

From which ye could not, etc. The law of Moses commanded what was to be done. It appointed sacrifices and offerings, as typical of a greater Sacrifice. But the same apostle has fully shown, in the Epistle to the Hebrews, that those sacrifices could not take away sin, Heb 9:7-14; Heb 10:1-4,11. The design of the law was not to reveal a way of pardon. That was reserved to be the peculiar purpose of the gospel.

The law of Moses. The commands and institutions which he, under the direction of God, established.

(c) "by him" Isa 53:11, Hab 2:4, Rom 3:28, 8:1