They can be the same when describing an action, one fits better than the other but they are the same in that way. But they can vary when describing an object, here's how they vary object-wise. (I tried my best when describing them.)

"How do you like..." is used to ask someone how they enjoy something or in which way something is prepared or what form it is in. In a conversation, it'll probably go something like this...

"How do you like your eggs, Name ?" Name answers, "I like them scrambled or over-easy." (Another example is, "How do you like your T-shirts, Name?" Name responds, "I like them cotton, not polyester.")

"What do you think of..." is used to describe your feeling toward a thing. The conversation in which that is used will probably go like this...

"What do you think of eggs, Person?" Person says, "I think eggs are gross, the flavor isn't good to me." (Another example is, " What do you think of T-shirts, Person?" Person explains, "I think that T-shirts are great, it just depends on the design, material, and time of year.")

Basically, material-wise, "How do you like..." is used to ask someone in what form do they enjoy something in or how they enjoy it. "What do you think of..." is asking their opinion of that said item.