No, the sentences in your image do not make sense. You are correct that “end up” is the correct way to phrase this type of sentence.

Suppose a dancing teacher has just explained to me how to do the cha-cha. I think I understand how to cha-cha but I feel uncertain about the final step. I could ask him "How do I end (doing) the cha-cha." The word "doing" is not needed in that sentence. It would sound strange to ask me how I ended meeting my wife because if I had ended the meeting, she wouldn't be my wife.