(B) will have been working
The sentence refers to a completed duration of action at a future point — requiring the Future Perfect Continuous tense (will have been working).
The phrase "by the end of this quarter" signals a future deadline, and "for eight months" shows duration — both together require Future Perfect Continuous: will + have + been + V-ing. Option (A) is Future Continuous (no duration marker used correctly); (C) is grammatically incorrect; (D) uses would, suitable only in conditional sentences.