The question you opened
Months that have 28 days
A calendar year runs from January through December.
How many months have 28 days?
All 12 of them
Every month runs past a 28th day, so every month has 28 days. February is simply the only one that stops there.
How many months have 28 days. All twelve of them. Every month on the calendar contains a 28th day, so every month has 28 days in it. March has 28 days and three more. July has 28 days and three more. February has 28 days and, in most years, nothing else. February is the only month that stops at 28, which is a different claim entirely. The question that February answers is: which month has exactly 28 days.
The word exactly does the work, and the puzzle wins by leaving it out. Your brain supplies it, because in ordinary speech a quantity usually means an exact quantity. If someone says they have twenty pounds, they rarely mean at least twenty. That gap between at least and exactly is worth more attention than a calendar joke suggests. It shows up in adverts offering up to 50% off, where up to is doing the same quiet work.
It shows up in job listings asking for five years of experience, in warranties covering repairs for two years, and in any claim about a minimum that reads like a promise about a total. There is a testing habit here too. Whenever a statement uses a number, ask whether it means at least this many, at most this many, or precisely this many. Three readings, and the sentence often supports more than one. If the difference matters, the ambiguity is the thing to resolve before doing anything else.
A last note on the calendar itself. In a leap year February has 29 days, which means it has 28 days as well as a 29th. The answer stays at twelve. And if you switch the question to how many months have 30 days, the answer is eleven, since February is the only one that stops short. The arithmetic is trivial. The reading is the puzzle, which is what makes it a good one.
Technique: Check for the word exactly