Indeed, the correct English phrase is 'to exchange greetings'.
The "correct" answer is not correct. It should be "I have exchanged greetings with the chief." Notice the plural. There is no place to report this otherwise.
The hint says "i have greeted" but when i put that its always marked wrong
'I have greeted' would be nimesalimia. Nimesalimiana means 'I have exchanged greetings'.