"He is extremely happy about that."
Translation:Li ege feliĉas pri tio.
I would expect pro rather then pri. 'That' is the cause, the motive of his being happy. 'Happy about' is a peculiarly English way of putting it, other languages have 'with' or 'through' or 'for'. I would hope for Esperanto to be more rigorous and logical here. Since 'pro' means caused by, motivated by', this seems to be the best preposition to go with 'happy'. This is only one instance in Duolingo where I feel that the Esperanto sentences have a distinctly English flavour. But perhaps this is something that Esperanto allows for: speakers of different languages giving their own native-language colour to their individual Esperanto?
You will find a lot of examples with "feliĉa pro …" You can be happy about the flowers and because of the love of your friend.
Your sentence is correct and—in my opinion—more common. But I think they wanted to show here that you can use an adverb (ege) before an adjective or before a verb.
For me as a native speaker of the German language feliĉi is much stronger than ĝoji. Please mind the spelling with ^.