"Buku ini ditulis anak-anak."

Translation: This book is written by children.

[CeoltoirAV]

So "oleh" is not necessary here after "ditulis"?

[joeldipops]

Yeah, oleh is normally optional. Though I assume required in formal contexts.

[Winmar]

Was written...

[Omariss]

Agree

[Geoffrey535218]

why cant: this book is written for children

[joeldipops]

Because that would need a different preposition, such as "buat" or "untuk"

[MikeWilby]

written for and written by are completely different meanings ----
by means that the children wrote it ----
--For means that someone wrote it for children to read