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By this they show
"By naturally obeying the law they show"
that the actions required by the law are written in their hearts
Here "hearts" is a metonym for the person's thoughts or inner person. The phrase "written in their hearts" is a metaphor for knowing something in their mind. You can translate this in an active form. AT: "that God has written on their hearts what the law requires them to do" or "that they know the actions that God wants them to do according to his law" (See: rc://en/ta/man/translate/figs-metonomy and rc://en/ta/man/translate/figs-metaphor and rc://en/ta/man/translate/figs-activepassive)
bears witness to them, and their own thoughts either accuse or defend them to themselves
Here "bears witness" refers to the knowledge they gain from the law that God has written in their hearts. AT: "tells them if they are disobeying or obeying God's law" (See: rc://en/ta/man/translate/figs-idiom)
on the day when God will judge
This finishes Paul's thought from Romans 2:13. "This will happen when God judges"