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).
What is the difference between Dein and Deine?
I think deine is femenine and dein masc & neutral. Plural is always deine
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 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.
Could deine blumen also be correct?
Yes, that's one of the possible translations.
Deine versus Eure?
"deine": one person
"eure": several persons
and "Ihre": one or several persons, formal
English does not differentiate here. All those are "your".