Which one is the correct form and why? Example sentence: x`
Katsumi has already lived in this twenty-four(-)hour KFC for two days.
Twenty-four-hour, because this is a compound adjective.
Compare it with the numeral, so that there's only one spot where you have to think about putting a hyphen, and the necessity should become clearer:
✗ Let's visit the 24 hour KFC.
✓ Let's visit the 24-hour KFC.