I wonder what would happened had he not taken the calligraphy course.
what would happened = why?
could you please tell me which part of this sentence is the noun clause ?
Is it a replacement of why?

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OK. It's good to see the original had the full "would _have_ happened." As for the inversion, that's one of the ways to make a question. A simpler sentence would be "I wonder what would have happened." That's complete on its own. The inversion is forced when one uses "had" as a way of saying "if." "Had he not taken the class" is the same as "if he had not taken the class"; "Had we not been there on time, she would have left without us" is the same as "If we had not been there on time, she would have left without us." Other words besides "had" that force the same inversion when used to replace "if" are "were" and "should": "Were we to go, we would dress nicely" is the same as "If we were to go, we would dress nicely" and "Should we drive, we'll take the dog with us" is the same as "If we drive (as opposed to walking, taking a bus, whatever), we'll take the dog with us."