You have my sympathy, because I believe the correct answer is East!
I don't think there is any difference between sunlight and moonlight, so I will just talk about the sun.
If you have impurities in the air, (eg dust or water droplets), and they are the same size or bigger than the wavelength of light, you get Mie scattering of sunlight.
Without getting too much into Mie scattering, an important feature is that a small deviation from the light's forward course is more common than a sideways deflection, and backwards deflection is rare.
The consequence of that is when you look up-sun, a large part of the air between you and the ground is scattering light at you. A lot of the ground features will have lower illumination than this scattered light, and you will not see them.
Although moonlight is weaker than sunlight, the scattered light is decreased pro rata with the light reflected off what you are looking for, so that makes no difference unless it is lit.
The more you look away from the sun, the less light is scattered back at you, and so visibility is reduced less. Looking away from the sun (or moon) is best.
In real life it is more complicated because it depends on what you are looking for. For example a lake can be easier to spot up-sun, but not an aircraft. Also many things are lit at night.
But if the exam question is as you stated, I would go for west. I would discard North and South as they are equally right and wrong, and all directions because it is silly.
Finally, after every PPL exam I took (FW and RW, ie at two different schools) an instructor went through each wrong answer with me. I thought they were supposed to.