Is this test question correct about the causes of detonation?
Yes, the writers of test questions are human too.  It would appear B and D are the correct answers.

According to the Lycoming website, for pilots, the greatest danger for detonation in aircraft engines is too lean a mixture.  Running rich at full throttle keeps cylinders cooler. Answer B is correct. Excessively lean mixtures can also be caused by clogged fuel injectors or air intake leaks.

Lower octane also increases risk of detonation because it's "autoignition" temperature is lower than higher octane fuel.  Autoignition can happen without spark due to higher temperature and pressure.  This throws the "timing" of piston power stroke and ignition off, causing a "ping" or "knock".  Engine damage may result. Answer D is correct.

So running rich at high power settings, while producing slightly less peak power, greatly extends the life of your all important engine.