The two motivating factors for the king to offer Douban great riches are A. Douban is an accomplished physician. and D. The king has a disease that no one can cure.
When the king was infected by leprosy, he could not find any cure until Douban came. After curing him, in gratitude, the king decided to reciprocate Douban's gesture with great riches.
This event is similar to the time Jesus visited Simon's house, and the mother-in-law was healed of her sickness, and she started to serve them.
Thus, we can conclude that the king was motivated to offer Douban great riches,in great appreciation of his healing, because of Options A and D.
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