"नेहा किताब लिख रही है ।"

Translation: Neha is writing a book.

[tulsihindi]

There is no एक, so shouldn’t it be “Neha is writing the book” ?

[zeebo7]

Sometimes the एक can be omitted if the meaning is clear. That is what's happening here.

[LornaMacC]

then why was it needed in "Peter's father is writing a book". I left एक out and it was wrong.

[LaviT333]

The book is not specified so the “ek” is unnecessary and as @zeebo7 said the word can omitted since it is rarely used because most of the times the meaning is clear.

[Shubhani_M]

I wrote "Neha's writing a book" and it said I had a typo. I think Duolingo needs to accept more casual language in its answers.

[talkingcentipede]

"Neha's writing a book" should also be accepted.