From the given sentence, form the feminine of the masculine word given:
The author was on the verge of a new idea.

The feminine kind of the word author would be, author + -ess, i.e., authoress. Therefore, option d is that the correct answer. Option a, writer is for somebody who writes, it should be a book, a commentary for a newspaper or anything. the author could be a synonym for the word author or the female of the author. Option b, Writeress is an incorrect word; there's no such word. the author may be a gender-neutral term. Option c, option poetess, is that the feminine sort of the masculine word poet. Therefore, option a, b, c, are incorrect.