I find 0.6763%
The probability for getting a BJ in 6-deck game is 0.04749.
The expected BJ hits are: 23.7447.
1 standard deviation from the expected BJ hits is 4.7557.
Thus, the deviation of expected BJ hits (23.7447) to 12 BJ hits corresponds to 2.4696 standard deviations or probability of 0.006763 or 0.6763% (once in 147.855 attempts).
My calculations apply for all naturals the player gets no matter if they push dealer�s BJs.