Questions & Answers about Ζήτησε συγγνώμη για την προσβολή.
Here Ζήτησε is the 2nd person singular aorist imperative of ζητώ.
So grammatically it is a command to one person: ask / request.
But in the fixed expression ζητώ συγγνώμη, it means apologize or more literally ask for forgiveness.
Because ζητώ συγγνώμη is a very common Greek expression.
- ζητώ = ask
- συγγνώμη = forgiveness, pardon, or sorry
So the whole phrase literally means ask forgiveness, but in normal English that is usually translated as apologize.
Greek does also have other ways to express apology, but ζητώ συγγνώμη is one of the most standard and natural ones.