Could you explain the difference between "When do you think he will come?" and "How do you think when will he come?". Why only the first one is grammatically correct and the second is wrong? Why can't I start it with how?
You are trying to translate the Russian "Как ты думаешь, когда он придет".
But you are doing it word-for-word. That is not how translation works. Not in this case, not in general. Doing that will always get you in trouble.
The English equivalent for "Как ты думаешь" is "what do you think", not "*how do you think". Or maybe "what do you figure", or "what would you say", or "what's your opinion" even. Or any number of others, really. But definitely not "*how do you think".
"How do you think" in English can be grammatical, but then it has a different meaning entirely. It is literally asking about the physical and chemical mechanisms and processes in the brain that we call thinking. The Russian equivalent to that would be something along the lines of "каким образом ты думаешь" or "как работает мыслительный процесс", or what have you.
So what you are asking in English, right now, is "Как работает твоя голова, когда он объявится?" Needless to say, that's a very funny question.