Of course you can just write anything to match the question, but in theory the answer should have existed before the question, so it should make sense on its own.
i think this was meant to be a shitpost and has no intended solution. out of all the crappy ones i could find on google this one makes the most sense, but given how there was probably no intended solution this one still doesn't make a lot of sense overall
Spoiler
its the letter f.
once a year: thats the f in Feburary
twice a month: the month has 4 weeks and the 2 f's are the First and Fourth weeks.
four times a week: the week has 7 days and the 4 f's are the First, Fourth and FiFth days.
six times a day: a day has 24 hours and the 6 f's are the First, Fourth, Fifth, Fourteenth, Fifteenth and twenty-Fourth hours (yes there are 2 f's in fifteen)