I think "public" should not be used as a noun when preceded by "more". "More public" has a meaning similar to "less private" - it's an adverb/adjective pair. I would not understand "more public" to mean "more common people" or "more of the public" as i think this Greek phrase is trying to say
Ok, there are two issues. First, the fact that the hints contain the word "audience" doesn't mean that it's correct here. Like a dictionary which may show many words as definitions but not all are suitable for each sentence...so always choose the first word that's how Duolingo is set up.
Second, you could use "audience" but you would have to say "larger" or "bigger".
The top hint is "more public".
The word "audience" is three rows down. This is how the Drop Down hints work.
Many translations may be given ... but not each one is possible for each sentence...just like any dictionary.
But Duo makes it easy for you by always putting the best translation at the top.
So, just use the top translations and you can be sure of always being right.