When you ask "How do you think?" You have to answer that I think with my brain or something. Moreover, maybe you would say "How can I do?" in "Chinglish", but the sentence is not correct and it should be "What can I do?". It's coincidental that I learned about it from a English-teaching program several days ago. So, I'm trying to answer you as a non-native English speaker. ～如有回答不完整，請多多包涵！

I agree with Sharonbee. 'How' is the way it is done and not the object. The sentence refers the the result of the thinking not the way. ie. Others think you are _________________. - and the answer could be - beautiful, wonderful, terrible, intelligent. etc. - - so it isn't important 'what' others think. It is true that you can say 'I don't like the way you think' = I don't like how you think' but it would be unusual to use it with an object ' I don't like how you think about me' In the same way on the sentence .- I eat ___________ - fish, potatoes, etc. you could comment 'what you eat is important for your health' - referring to the objects that you eat. is different to 'how you eat is important for your health' - the way you eat. I hope the examples serve to clarify and not to confuse you more!

I'm sure there are rules that would explain why C is wrong. But A is the correct answer. It just sounds more natural.

A, no other answer.