By the end of 2013, roughly
31.09 million units (1) were sold under the 3DS umbrella (including the 2DS sand 3DS XL); likewise, by the end of 2013, roughly
11.61 million units (2) of Pokémon X and Pokémon Y had been sold, including a 4 million unit launch weekend (3). By using figures 1 and 2 (note that the same figure for end of year system sales has been used here; a smaller install base at launch would mean a greater multiplier, but I'm just going off the statistics I can find), we can estimate that approximately 13% of the install base purchased XY on the launch weekend, and, by using figures 1 and 3, that approximately 37% of the install base had purchased the games by the end of 2013.
Now, we don't know exact figures, but we do know that Pokémon Sun and Pokémon Moon are the
most pre-ordered Nintendo games to date (though I can't use this in my calculations, I can in my personal predictions). The 3DS install base has obviously grown since the launch of XY, and, in fact, it has more likely more than doubled,
passing 60 million units worldwide as of June 2016. Yeah, you know,
before the unanimous success of GO? Anyhow, let's keep conservative and say they haven't sold a single system since that day and keep that figure at 60 million systems sold to keep it simple. By using the multipliers above, we can estimate that 13% of the 60 million system install base will purchase the game over the launch weekend, giving a total of about 7.7 million units over the weekend. Now, using the 37% multiplier, we can estimate that approximately 22 million units could end up being sold by the end of December 2016 (note here that the games will have been on sale a month less than XY, but considering it is much closer to Christmas I think the same multiplier could remain in effect). This would make it the third highest selling pair of Pokemon games in history, behind GS (23.1 million units sold) and RGB (31.38 million units sold), and that's without taking into account what happens
after 2016. XY is currently sitting at 15.64 million units sold at the end of its generation, 3 years on, and we can find this to be a multiplier of roughly 135% of the games sold of XY by the end of 2013; applying that here would give a total of roughly 30.25 million units sold at the approximate end of Gen VII! Of course this doesn't take into account the Switch or other deterring factors, but, likewise, these calculations didn't take into account positive factors such as the effect of GO, a larger install base than used, etc. And please do note that these are just simply calculations; they could be well off, which is why I'm going to include some different views below.