What day is the next meeting?
how many days
Asks about a duration or number of days. Often used with counters or in expressions like 何日間.
About how many days is the trip?
For how many days did you take this medicine?
What's the date today?
How many days does it take to walk from Tokyo to Osaka?
How many days are you planning to travel for?
How many days has it been since he was born?
何時間 asks how many hours something takes, whereas 何日 asks how many days (or which day of the month), so they're easy to mix up when asking about time spans.