1. What do you think of?
2. How do you think of?
I think "of" is a preposition, after which we should use a noun or a pronoun. Therefore, the second sentence is incorrect.
Is my understanding right?
Well, both sentences are incorrect.
'What do you think of...' needs a subject. What do you think of it? What do you think of him? etc.
'How do you think...' is just a strange construction in English that cannot be used to ask someone's opinion. It asks about the mechanics of thinking; how do you generate thoughts, how do you as a person think, not what is your opinion. It is a very common error, especially by those whose first language is Mandarin.
if "of" is a preposition, prepositions need to be followed by a noun. So the sentence "What do you think of..." Needs to be ended with something like "what do you think of (it)?" So yes, the second sentence does not make sense it is incorrect.
