Hey there! I’m happy to help!
Let’s see what each of these eras are.
The Old Kingdom of Egypt is basically the time period when the pyramids were built.
The Middle Kingdom is known for a lot of Egyptian art and literature being created.
The reign of Hyksos was a period after the middle period when the Hyksos had invaded Egypt where the Egyptians didn’t really do much.
The New Kingdom was basically when Egypt became super imperialistic and started taking everything over.
If you look at all of these, it makes the most sense that The Sphinx was built during the Old Kingdom because it was actually built for one of the pyramid builders!
I hope this helps!
