Okay, I think I understand this now. If you can read Italian, have a look at this discussion:
When you use "entro" with a unit of time, you are treating that unit as if it were indivisible. Unless there is other evidence in the context, you haven't said whether you'll go before June 1 or if you mean you'll go before June 30.
The best English might be "We'll go before some time in June."
This is, I think, tied to the same notion of treating time as a unit vs. treating it as a duration that influences the use of the imperfetto vs the passato remoto/prossimo.
Here's the entro entry from a big Italian-only dictionary:
Entro: prima della fine di: e. un mese, e. quest'anno; te lo manderò e. domani
That means "before the end of", sometimes reducible in English to "by" or (easy to remember from the meaning of dentro) "within / inside".
There are no alternative definitions - it means this and nothing else. Much speculation below is wide of the mark, and so too is Duo's "before June".
From the Wordreference discussions, I'd say the closest translation is 'we go BY June'. This handily provides the same slight uncertainty as to whether the speaker means 'before June starts' or 'before June ends.' Clearly not a great choice of phrasing in either language.
This problem came up before in another context and I got it wrong again by using the "within" sense of entro but changing it to make sense in English (We go in June). It makes no sense to accept "within June" but not "in June" since the former is nonsensical in English. Either they should not accept any variation of "within" or they should accept the ones that actually translate into English.
does 'giunio' mean something else? sometimes it allows misspellings and sometimes it punishes you, and in this case it is marking it wrong rather than just pointing out the spelling error. the difference seems to be whether the misspelling could be another word...
That is a creative translation buwaya - but it seems to suggest going at the start of June, which is not what either the meaning of "before" or "within" suggests. My question is more basic: Isn't it confusing to have an expression which can mean both of these things? Arranging your holidays must be a nightmare!!
I think the better translation for "let's go come June" is "Andiamo arriva giugno". So it won't really work here. Contextual meaning here in Duolingo is sometimes lost while the owl is watching.
Consulting http://forum.wordreference.com/showthread.php?t=1579089, I found that "entro" is really ambiguous even for Italians.
Maybe the better phraseology here is "Andiamo davanti a giugno" if we are to use the word "before".
Se la frase é scritto cosi, arriviamo con una frase piu chiare.