"Your men are strong."
Translation:Eure Männer sind stark.
deine is for a feminine or plural noun that belongs to du (to one person that you are speaking to)
eure is for a feminine or plural noun that belongs to ihr (to several people that you are speaking to).
It's like the difference between "his" and "their", or between "my" and "our" -- whether the possessor is one person or several people.
No: it's not masculine, it's plural.
There are no gender distinctions in the plural in German. It acts a little bit like a fourth gender: masculine, feminine, neuter, and plural.
You need deine before any plural noun: deine Männer, deine Frauen, deine Kinder. Regardless of what gender the singular would be (der Mann, die Frau, das Kind).
They do when they are attributive adjectives (basically: when they are before a noun).
They do not when they are predicative adjectives (basically: when they are after the verb "to be").
And before the noun, they can change the form based on gender/number/case in one of three different ways, depending on what's in front of them.... (Though one of those three is just a mixture of the other two.)
For example: der gute Wein, mit dem guten Wein; guter Wein, mit gutem Wein; ein guter Wein, mit einem guten Wein. And so on for the other genders (feminine, neuter, plural) and cases.
mann and männer are not German words. I think you are looking for Mann and Männer (capitalised) -- that word can indeed be translated as "husband, husbands" in a possessive context.
So eure Männer could mean "your husbands" (when you are speaking to several people, and presumably each of them has one husband each).
ihr means "her" or "their", not "your".
If you were trying to use the polite possessive for "your", that would be Ihr -- capitalised.
But since Männer is plural, the possessive needs to be Ihre with the plural ending -e: Ihre Männer sind stark. (Which is one of the accepted alternative translations.)
Question 1: How do I know if its "dein" or "deine"?
Use dein before masculine or neuter nouns in the nominative case, or before neuter nouns in the accusative case.
Use deine before feminine or plural nouns in the nominative or accusative cases.
Use deinen before masculine nouns in the accusative case.
(The gender of a noun is something you have to learn and memorise.)
Question 2: How do I know if its "deine" or "eure"?
Use dein, deine, deinen when you are talking to one person.
Use euer, eure, euren when you are talking to several people at once.
Usually, in a Duolingo sentence without context, you can't tell whether "your" is talking to one person or several people, and so either translation will be accepted (as long as the ending is appropriate for the following noun).