What is a good hook for a compare and contrast essay about the religious and economic styles of Ancient Egypt and Ancient China?

First, you will have to look at religion and economics in both ancient Egypt and ancient China.  In Egypt, the religion was a polytheistic one.  Egyptians worshipped many gods for many purposes.  The pharaoh was considered to be a divine figure, who served as an intermediary between the gods and the Egyptian people.  The Egyptians had a much stronger belief in an afterlife than the Chinese did.  In China, the main religion was one that became what is now Taoism.  This was also a polytheistic religion.  It was partially influenced by Chinese dependence on shamans.  The focus is on oneness with nature and on balance.  Both religions shared similar deities, such as gods of Sun and Earth.  

Trade was important in both ancient Egypt and China.  Silk was a major export from China.  Some merchants traveled by water to sell their goods.  Others used the Silk Road as a land route for trade.  In Egypt, merchants sold gold, papyrus, and linen.  Merchants used the Nile River to travel.  Some even visited port cities along the Mediterranean Sea.  Both economies also relied heavily on farming.  In China, salt and iron were mined.  In Egypt, mining was focused on gold and various types of stone.

You can look at this information and what each culture had in common.  You can also see what they did not have in common.  From there, you can decide what your hook will be.  An example might be:

"Though they were thousands of miles apart, Ancient Egypt and Ancient China had much in common.  Their economies relied heavily on trade and their religions were both polytheistic.  They did have some differences, such as the Egyptian reliance on water routes for trade and the Chinese dependence on the Silk Road."