Each of the four cases belongs to a distinct, well-known area of public law, so the question can be answered by matching subject matter to the specific dictum quoted rather than by simply recalling one fact in isolation.
Since the quoted words belong to a habeas corpus judgment, and only Greene is a habeas corpus case among the four, the case being referred to is Greene v. Secretary of State for Home Affairs (1942) AC 284.
A useful way to answer this is to set Greene directly against its closest rival, Bugdaycay, since both cases involve the Home Secretary's power over a detained or threatened individual, before disposing of the two clearly unrelated options.
Once Bugdaycay is separated from Greene on the ground of habeas corpus versus ordinary judicial review, and the other two options are excluded as belonging to unrelated doctrines, Greene remains the only case matching the quotation.
Therefore, the correct answer is Greene v. Secretary of State for Home Affairs (1942) AC 284.