“Why can I” is the correct structure when you are asking a direct question. When asking a direct question you always change the order of the subject and the main verb.
“…..why I can” could also be correct if the question is an indirect question. An indirect question has some additional words before “why I can” and is a way to be more polite in English.
Why can I not overtake here?
Would it be possible for you to tell me why I can not overtake here?
Notice that both examples have the same intention but the second example adds extra information.
Why can I?
“Why can I?” is correct Why it comes at the beginning of the sentence.
Why can I not take the train?
Why can I not start a business?
Why can I buy beer in this store and not the other?
Why I can?
“Why I can” is correct Why it forms part of an indirect sentence.
Do you mind telling me why I can’t find a tennis court that is open?
Could you tell me why can’t I fix my phone?
Would it be possible to know why I can’t see a doctor?
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