They don't really make sense without something after the "of". "what". Share your opinion in general "How" share your thought process used to form an opinion/answer.

"What do you think of..." is very common and frequently used in ordinary conversation. Following "What do you think of...," I expect to hear the name of something. The speaker wants to know my opinion. "What do you think of Starbucks' coffee?" "It's overpriced." "How do you think of..." would be rare, and it means something completely different. Following "How do you think of..." I would expect to hear a word like "ideas" or "stories" or "tunes." "We're excited to have Taylor Swift on our talk show today. My first question, Taylor, is: how do you think of ideas for song lyrics?" "How do you think of ways to entertain the grandchildren on Thanksgiving?"