Well "leisurely" is an adjective, just the wrong one. "Idle" would be better here.
While technically "leisurely" can be an adverb too, I've rarely heard it used that way. I've even heard people say "leisurelily" because "leisurely" just doesn't sound right somehow: They walked home leisurely.
I think what they are looking for here (as with the question about the "feminae otiosae" writing letters) is not that he is reading a book in an unhurried manner or without haste (leisurely), but that he is an "old man at leisure", i.e. free from duties and responsibilities - because of retirement and/or wealth which enables him to own slaves.
I thought the same thing - I was marked wrong in a similar sentence about leisurely old men. I'm not sure what they are...
Contributors: I reported the hover hints incorrect because there was no option to report the English as questionable.
I think this should read The old man leisurely reads a book
If I didn't know the Latin was an adjective, I'd be more inclined to move the tiles so the translation says ""The old man leisurely reads a book."
But "leisurely" is both adjective and adverb despite its spelling.
I don't have a problem with a leisurely "walk" or "bath" but calling a man, whatever his age, "leisurely" just sounds wrong. It seems to defy logic.
I know Duolingo doesn't want every possible synonym in English, but "unhurried old man" or "laid-back old man" would sound better to me.
I think the course's intention might be to highlight the contrast between negotiosus (busy) and its antonym otiosus (not busy), both of which are introduced in these exercises. The trouble is English doesn't really have a suitable adjective for "not busy". "Idle" is the closest we have, but even that has some negative connotations (lazy/shirking) that are not present (at least to the same extent) in "otiosus".
"Inactive" and "sedentary" don't really work. Perhaps "unoccupied" is a bit better than "idle"?