Some online sources report 8 previews. According to Variety, however, there were 14, starting on Tuesday, December 25, 1962. There were 6 previews during the first week, and 8 during the second week. Variety was sometimes mistaken about such matters, but the paper seems to have been correct on this.
The production had originally been scheduled to open on Thursday, December 27. Producer David Merrick postponed the opening till Sunday, January 6, in the hope that the strike against New York newspapers that was then in progress would be resolved by that date. It wasn't.
At the time, it was unusual for a Broadway show to open on a Sunday. According to Variety, the reason that the rescheduled opening was on a Sunday was "to avoid a reshuffling of performances which have already been sold." The show was heavily pre-sold to theatre parties, and it played to capacity houses during previews.
It seems likely that there was no preview performance on the date originally scheduled for the opening. This would explain why the production played 6 previews rather than 7 that first week.