Q: Is it possible to move the Solemnity of the Epiphany which is on 6 January 2021 to 2nd Sunday in Christmas Time 3 January 2021 which I believe is within the Octave of Christmas.
Also I note some calendars have put Epiphany on 3 January 2021: the Philippines, Hong Kong and the USCCB. The UK one remains at 6 January.
I have the understanding that the feast is moved to the nearest Sunday every time it falls on a week day, this is to allow people to celebrate the feast. Hence, the research on what conferences would do next year as it is within the Octave of Christmas.
A: Canon 1246 §1 lists the days that must be observed as days of obligation though §2 allows conferences of bishops to suppress certain days with approval of the Apostolic See. The ten days include the Epiphany.
Where the Epiphany is observed as a holyday on January 6, the preceding Sunday is usually the Second Sunday of Christmas.
The Roman Missal says that wherever the Epiphany is not kept as a holyday of obligation (a day of precept) on January 6, it is assigned to the Sunday that falls from January 2 to January 8. That way the entire Catholic community holds Epiphany as a day of precept, though some observe it on a Sunday. In those conferences, the Second Sunday of Christmas is never observed.
If you reside in the territory governed by a conference of bishops that has kept Epiphany as a holyday of obligation on January 6, then you may not move it to Sunday. The decision pertaining to the date of the Epiphany is made by your conference of bishops in conjunction with the Vatican.