16 days you work with 14 off, 15 off or 12 off depending on whether it's a 30, 31 or 28 day month. "Normally" they say 30 days to a month. On average 365 1/4 days divided by 12 is 30.4375 days in a month which is closest to 30.
That's if the 4-4 cycle starts on the 1st day of the month
On average, you'll work 15, 15 1/2 or 14 days a month, if it's a 30, 31 or 28 day month and the 4-4 cycle doesn't necessarily start on 1st of the month. 15 days would be a good answer.
That's if you count a work day as any day you do any work, including just 4 hours.
But you really worked 12 hours each day, and you could define the "work day" as a 12 hour work day, or as an 8 hour work day, or a full 24 hours. Work 16 hours a months is 1 1/2 days of 12 hour shifts
or 16/24 = 2/3 day of 24 hour day's work Or 15/24 = 5/8 of a day.
A "normal full time work day" though is 8 hours, 16 hours is then 2 normal work days a month.
All in all, 15 or 16 look like the best answers. Unless there's more context to this question, not given.
Depending on how you define, month and "day" in terms of hours or "work hours," the solution could be anywhere fro 5/8 of a day to 16 days.
