When asking about a specific date, both ‘what date’ and ‘which date’ can be correct, but they are used in slightly different contexts.
‘What date’ is generally used when you are asking for a date in an open-ended manner, without any specific options in mind. For example, ‘What date is the meeting?’ implies that you are asking for the date without any prior knowledge of possible dates.
‘Which date’ is used when you are choosing from a set of known or implied options. For example, ‘Which date works best for you: the 15th or the 20th?’ implies that you are asking the person to choose between specific dates.
In summary, use ‘what date’ when you are asking for a date without any specific options, and use ‘which date’ when you are choosing from a set of known dates.