The numbers are 1, 3, 5, 7, 9 and 11!
Explanation:
Once in a year = 1 (One new year in one year) Take out 12.
Twice in a month = 1, 3 (1+3 = 4 weeks. 2 fortnights in one month) Take out 2, 4 and 8.
Four times a week = 1, 2, 3, 4, 5, 6, 7 (Monday to Sunday) Take out 4.
Six times a day = We get 4 new hours 6 times a day (24 hours). 12 hours = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Take out 4, 6 and 10.
The remaining numbers are 1, 3, 5, 7, 9 and 11. Once you extract all the unnecessary numbers, the odd numbers remain.
Good luck with you studies!