The correct answer is: C. have been writing
The verb “write” is an action verb, which means that it describes an action that is being performed. In this case, the action is “writing a book.” The sentence “I have been writing this book for the last four years” tells us that the action of writing the book has been going on for a long time. This is why the correct answer is “have been writing,” which is the present perfect continuous tense. The present perfect continuous tense is used to describe an action that has been going on for a period of time and is still going on.
The other options are incorrect because they do not accurately describe the action of writing the book. The verb “write” is not an infinitive verb, so option A (“write”) is incorrect. The verb “writing” is not a gerund, so option B (“writing”) is incorrect. The verb “has writing” is not a verb phrase, so option D (“has writing”) is incorrect.
In conclusion, the correct answer to the question “I . . . . . . . . this book for last four years” is C. have been writing.