The correct answer is A. Jonah has two ultimate goals: becoming a published columnist and writing a book.
When a sentence contains parallel structure, that means that the same form of a word is used throughout. In sentence A, as you can see, the same form of a verb is used - both verbs (becoming and writing) end in -ing. There is no mixing of forms (like in the other options), which is why only A contains parallel constructions.
