I looked this up quite a bit, and most people seem to think the answer is "odd numbers".
Let me explain:
Because the number of months in a year are 12, we can take the two numbers in 12 (1 and 2).
(1), 2 = 1 odd number
So, once in a year.
In a month, there are four weeks. So we take the four numbers leading up to four (1, 2, 3, and 4).
(1), 2, (3), 4 = 2 odd numbers.
So, twice in a month.
In a week, there are seven days. So we take the seven numbers leading up to seven (1, 2, 3, 4, 5, 6, and 7).
(1), 2, (3), 4, (5), 6, (7) = 4 odd numbers.
So, four times in a week.
Finally, in a day, the people who have answered this question before seem to assume that there are 12 hours during daytime. We can take all 12 numbers leading up to 12 (1, 2, 3, 4 ... 12)
(1), 2, (3), 4, (5), 6, (7), 8, (9), 10, (11), 12 = 6 odd numbers
So, six times in a day.
I'm not entirely sure that this answer is correct, because there are a few assumptions we had to make, but this is the best answer I could find.
Hope this helps :)