Does the time difference between Manila and New York change during the year?

Yes. Because of daylight saving time the gap moves between +12h and +13h.

When is the best time to call New York from Manila?

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

Manila is 12h ahead of New York. This gap is not fixed: daylight saving time moves it between +12h and +13h during the year.

Manila

Philippines

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New York

United States

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

City	Time zone	UTC offset
Manila · Philippines	Asia/Manila	UTC+8
New York · United States	America/New_York	UTC−4

What is the time difference between Manila and New York?: Manila is 12h ahead of New York. This gap is not fixed: daylight saving time moves it between +12h and +13h during the year.
Does the time difference between Manila and New York change during the year?: Yes. Because of daylight saving time the gap moves between +12h and +13h.
When is the best time to call New York from Manila?: There is no overlap between standard working days, so one side has to call early or late.