Does the time difference between Cairo and Seoul change during the year?

Yes. Because of daylight saving time the gap moves between −7h and −6h.

When is the best time to call Seoul from Cairo?

Between 09:00 and 11:00 in Cairo, which is 15:00 to 17:00 in Seoul.

Cairo is 6h behind Seoul. This gap is not fixed: daylight saving time moves it between −7h and −6h during the year.

Cairo

Egypt

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Seoul

South Korea

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A 9-to-5 day in each city overlaps for 2h. That is 09:00–11:00 in Cairo, which is 15:00–17:00 in Seoul.

City	Time zone	UTC offset
Cairo · Egypt	Africa/Cairo	UTC+3
Seoul · South Korea	Asia/Seoul	UTC+9

What is the time difference between Cairo and Seoul?: Cairo is 6h behind Seoul. This gap is not fixed: daylight saving time moves it between −7h and −6h during the year.
Does the time difference between Cairo and Seoul change during the year?: Yes. Because of daylight saving time the gap moves between −7h and −6h.
When is the best time to call Seoul from Cairo?: Between 09:00 and 11:00 in Cairo, which is 15:00 to 17:00 in Seoul.