Is there any reason why this could not also be "Deine Blumen"?
It could be, in fact it was my answer which duolingo accepted
Depends only on the context
When is it Deine and when is it Eure???
It's deine when it belongs to one person, I.e 2nd person singular, and eure when it belongs to many people, I.e 2nd person plural.
In short, du > deine, ihr > eure
When is eure and eurer used?
But why it is showing ihre in my answer?
ihre (lowercase) would be wrong but Ihre (capitalised) is possible -- that's the possessive form of Sie (formal you).
Why isn't "euere" accepted when "eure" is a shortened version of "euere"?
euere is rarely used -- so rarely that it sounds wrong to me.
You can report it if you'd like.
What is the difference between Dein and Deine?
I think deine is femenine and dein masc & neutral. Plural is always deine
What is the difference between ihr and eure ?
Why wouldn't this sentence be deine Blumen?
"your" can be "deine", "eure" and "Ihre", depebding on whether you speak informally to one person, several persons, or formally. All three versions are accepted.
Duo is telling me the answer is "Deine Blumen" but Deine was not even an option.... I took a screen shot if anyone is interested.
English "your" is ambiguous. It can be "deine", "eure" or "Ihre" in German. One of these was certainly an option.