"let me know what do you think" or "let me know what you think" I would say the second one sounds more natural but they both mean the same thing. I would stick with the second one because in the first one it sounds a little fragmented (broken up) I hope you get what I mean and I hope I have helped some

My own typo correction: "...it isn't used by English speakers."

"Let me know what do you think" isn't grammatically correct and it isn't used my English speakers. It's a bit of a stretch, but you could use these as two different sentences in short conversation, like texting for instance. Example: What do you think? Let me know. But overall, it would be best to stick with "Let me know what you think."

For the phrase ' let me know what do you think ' , this is question form. And the phrase ' let me know what you think' is affirnative form. Hope it help