V-게 하다
This pattern means to make, let, or have someone do something. It is formed with a verb stem + -게 하다. In the story, "선생님은 자기소개를 하게 했다" means the teacher made him do a self-introduction. You can reuse it in class or everyday situations: "선생님은 학생들에게 자기소개를 하게 했어요."
선생님은 학생들에게 자기소개를 하게 했어요.
The teacher had the students introduce themselves.
