Which of these is correct and why?
However, after a few hours of opening an incident occurred.
However, a few hours after opening an incident occurred.
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Depends on context.
The form "after a few hours of opening" seems to imply that the process of opening had been ongoing for a few hours. It might be the case for a flower, for example, where the process can take hours.
The form "a few hours after opening" would be appropriate in, for example, the case of a store opening at 9AM. A few hours later something happened.