How many months have 28 days?

All twelve months have 28 days.

While it is true that Feb has precisely 28 (or 29) days, the question in this post is usually intended as a trick riddle.

The answer to that riddle is "all 12 of them".

All months in both the Gregorian and Julian calendars have 28 or more days. The details are:

The Gregorian calendar has four months with a length of 30 days and seven months that are 31 days long. February is the only month that is 28 days long in common years and 29 days long in leap years.
The 12 Months of the Year
The Gregorian calendar and the Julian calendar both consist of the following twelve months:
January - 31 days
February - 28 days; 29 days in Leap Years
March - 31 days
April - 30 days
May - 31 days
June - 30 days
July - 31 days
August - 31 days
September - 30 days
October - 31 days
November - 30 days
December - 31 days

http://www.timeanddate.com/calendar/months/

The question actually has many ambiguities we can examine.
(Yes I'm aware this is a popular 'gotcha' riddle, but there is much more than meets the eye here)

I'll assume for the sake of brevity that a 'day' refers to one Solar day on Earth; about 86,400.002 seconds in recent decades. Otherwise, we'd be able to make some really wacky answers!

If we're talking about Lunar months there are 5 ways to define this, each with a different duration (see table below), none of which are exactly 28 days. However, anomalistic Lunar months would round to 28 if we're looking only at 2 significant figures. So I guess that makes every anomalisitic month 28 days. Is the question asking for how many anomalistic months there are? That would be a difficult question to answer.

Month type: Length in days:
draconitic 27.212220815
tropical 27.321582252
sidereal 27.321661554
anomalistic 27.554549886
synodic 29.530588861
(there is a small correction factor involved in each depending on what year we're looking at)

https://en.wikipedia.org/wiki/Lunar_month

If instead the question is referring to months in the Gregorian Calendar (as opposed to any number of other calendars we may look at, some of which are still used contemporarily), it is of course true that there are at least 28 days in all twelve named months. It's not clear to me, however, that this is the same as 'having' 28 days. Would we also say every month has one day? Perhaps this works for some but I find it a bit silly.

There are so many other lines of exploration of this question but I'll leave it there. "February in non-leap years" works for me. But hey, if you really wish, there is probably a valid way to make a 'month' 'have' however many 'days' you want it to have. The universe is your oyster!