I don't think Multiple Choice has a formula field version, but you could set it as a formula text with this formula (not tested):
If(
not IsNull([Date 4]), "4th",
not IsNull([Date 3]), "3rd",
not IsNull([Date 2]), "2nd",
not IsNull([Date 1]), "1st"
)
In this case, it will check [Date 4] first and if its filled in, it will output the text you want in place of "4th."
If you still wanted it to be a multiple choice field, you could set up an automation or action for this where when [Date *] gets filled in, input "1st, 2nd, 3rd, or 4th" in your multiple choice field, but that won't have the precedence requirement, so I think the formula text is your best bet if you want it to be completely automated.
