Does the time difference between Hong Kong and Rome change during the year?

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

When is the best time to call Rome from Hong Kong?

Between 15:00 and 17:00 in Hong Kong, which is 09:00 to 11:00 in Rome.

Hong Kong is 6h ahead of Rome. This gap is not fixed: daylight saving time moves it between +6h and +7h during the year.

Hong Kong

Hong Kong SAR China

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Rome

Italy

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

City	Time zone	UTC offset
Hong Kong · Hong Kong SAR China	Asia/Hong_Kong	UTC+8
Rome · Italy	Europe/Rome	UTC+2

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