Question

It said Pokemon sun and moon came out on 12/31/16 fom a gamestop book is that correct ?

Comments

Official statements from Nintendo and the Pokemon Company say that they will be released in "holiday 2016". Retailers like Gamestop might have further knowledge regarding this, but we don't know for sure; that date may or may not be accurate. At this early stage, a specific date may not exist.
Personally, I doubt that's the real date, because a December 31 release would be stupid from a business perspective. A release before Christmas is always optimal and is probably what you can expect from these games.

Answer 1

Pokemon Sun and Moon came out on November 18th, 2016 everywhere in the world except for Europe, where they came out November 23rd, 2016.
December 31 was likely listed as the release date because the official release date had not been announced. Best for distributors to assume the release date is later rather than earlier.

Answer 2

It is a widely used placeholder date for the big Christmas titles across the industry. It will most likely be changed to an earlier date, as early as Black Friday, as we get more information closer to the release.