Correct Answer - `.^(12)C_(2)xx(2^(6)-2)`

Any two months can be chosen in `.^(12)C_(2)` ways. The six birthdays can fall in these two months in `2^(6)` ways. Out of these `2^(6)` ways there are two ways when all the six birthdays fall in one month. So, the required number of ways is `.^(12)C_(2)xx(2^(6)-2)`.