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Is it correct if I say "I have lived in Cairo since four years ago" or we can't use "ago" with the present perfect tense?…
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It is possible to say I have lived in Cairo since four years ago. The understanding here is that the beginning of the period was four years ago. Remember that we use since to talk about the beginning of a period.
However, this structure is rather rare, and it might not be recognized as correct on an exam. I think it would be better to avoid it and to say I have lived in Cairo for four years.

What's the difference
I have been to Aswan .
I have gone to Aswan.
I have been in Aswan.