Day of Arafah based upon local mooon sighting

Shaykh Ibn ‘Uthaymeen رحمه الله was asked:
What if the day of ‘Arafah is different because of the moon being sighted at different times in different countries? Should we fast according to the moon sighting in the country where we are or according to the moon sighting in al-Haramayn (the two Holy Sanctuaries)?
He replied:
This is based on a difference of opinion among the scholars. Is there only one moon sighting for the whole world or does it vary according to when the moon rises in different places?
The correct view is that it varies according to when the moon rises in different places.
For example, if the moon is sighted in Makkah, and today is the ninth, and it is sighted elsewhere one day before Makkah, and the day of ‘Arafah in Makkah is the tenth for them, it is not permissible for them to fast on this day because it is Eid.
Similarly if it so happens that they sight the moon after Makkah, and the 9th in Makkah is the 8th for them, then they should fast the day that is the 9th for them, which is the 10th in Makkah. This is the correct view, because the Prophet صلى الله عليه وسلم said: “When you see it (the new moon) fast and when you see it break your fast.”
Those who did not see the moon in their own location have not seen it. Just as people are unanimously agreed that the times for dawn and sunset vary according to their own location, so too the months are also worked out by location, just like the daily timings.