Translation:They announce your book.
"their book" should also be OK I suppose? though not accepted
that's ok too!
But isn't it more common in Brazil to say "their book" as "o livro delas"?
Yes, but seu/sua = your, his, her, its, their, so his answer is still right.
Why not, " Elas anunciam seus livros. " ?
That is "your books".