An embedded question with -는지 plus 보여주다 means showing someone what or how, rather than telling them. Every line here uses 보여주다 or 보여드리다 rather than bare 보이다, and most begin with 어떻게: 어떻게 하는지 보여줄게 (I'll show you how it's done), 복구한 다음에 어떻게 됐는지 보여드릴게요. It is the standard promise a demonstration video makes.