Per the official chronology, it's 12 years, since they put TWOK in 2385, 18 years after "Space Seed" instead of the stated 15, for some strange reason that even Mike Okuda no longer remembers (I asked him). My best guess is so that TFF would be 20 years after "Balance of Terror" to be consistent with the stated age of Nimbus III, though why they chose to fudge TWOK's date instead of that date is a mystery.
I wonder if placing TWOK in 2285 has something to do with the Romulan Ale McCoy gave Kirk, which was a 2283 vintage. Could Okuda wanted to place it sometime after that?
It'd probably make more sense to fudge TFF timeline. I mean, they could say they were just rounding the age of the settlement at Nimbus IIII to 20 years since it was close to that anyway. And Khan being a superman he would probably remember the exact years a little more clearly.
At the end of the day someone didn't do their homework when they were checking their timelines
. If TWOK was meant to take place in 2283 then Nimbus III should have been 18 years old. Though to be completely fair there was no Memory Alpha back then to check this stuff and we weren't firmly settled yet on the timeline of the original series (I think it was settled to the late 2260s by then, just not exact years yet since Q2 was still years from airing).