Why not "ayıdır" ?
Yil is year, what is yilin? And what does the "in" suffix in general?
in Turkish both the possessor and the possed thing gets a suffix. So -in here is the genitive suffix. These are already explained in tips¬es ;) https://www.duolingo.com/skill/tr/Possessives
And it takes the possessive since it's "of the X".
''Ağustos sekinci ay yılındır'' should be accepted ?
Or maybe saying ''Ağustos yılın sekizinci aydır''?
Yes it it 'sekiz' so 'sekizinci'