Peter gives examples of people who acted against God and whom God punished because of what they did.
"did not refrain from punishing" or "punished"
The word "Tartarus" is a term from Greek religion that refers to the place where evil spirits and wicked men who have died are punished. AT: "he cast them into hell" (See: rc://en/ta/man/translate/translate-names)
This can be stated in active form. AT: "where he will keep them in chains of lower darkness" (See: rc://en/ta/man/translate/figs-activepassive)
Possible meanings are 1) "in chains in a very dark place" or 2) "in very deep darkness that imprisons them like chains." (See: rc://en/ta/man/translate/figs-metaphor)
This refers to the day of judgment when God will judge every person.
Here the word "world" refers to the people who lived in it. AT: "he did not spare the people who lived in the ancient world" (See: rc://en/ta/man/translate/figs-metonymy)
God did not destroy Noah and seven other people when he destroyed the rest of the people who lived in the ancient world.
"burned the cities of Sodom and Gomorrah with fire until only ashes remained"
Here the word "them" refers to Sodom and Gomorrah and the people who lived in them.
Sodom and Gomorrah serve as an example and a warning of what will happen to others who disobey God.