Does the time difference between Dubai and Vancouver change during the year?

Yes. Because of daylight saving time the gap moves between +11h and +12h.

When is the best time to call Vancouver from Dubai?

There is no overlap between standard working days, so one side has to call early or late.

Dubai is 11h ahead of Vancouver. This gap is not fixed: daylight saving time moves it between +11h and +12h during the year.

Dubai

United Arab Emirates

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Vancouver

Canada

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A 9-to-5 working day in Dubai does not overlap one in Vancouver at all — somebody has to take the call outside office hours.

City	Time zone	UTC offset
Dubai · United Arab Emirates	Asia/Dubai	UTC+4
Vancouver · Canada	America/Vancouver	UTC−7

What is the time difference between Dubai and Vancouver?: Dubai is 11h ahead of Vancouver. This gap is not fixed: daylight saving time moves it between +11h and +12h during the year.
Does the time difference between Dubai and Vancouver change during the year?: Yes. Because of daylight saving time the gap moves between +11h and +12h.
When is the best time to call Vancouver from Dubai?: There is no overlap between standard working days, so one side has to call early or late.