Datediff by column values

This will get you started:

Appointment Date Diff = 
--VAR CurrentAppointmentType = MAX('Table'[Appt_type])
VAR CurrentCustomer = MAX('Table'[Customer])
VAR AppointmentCustomerGrouping64 = 
    FILTER(
        ALL('Table'),
        'Table'[Appt_type] = 64 && 'Table'[Customer] = CurrentCustomer
    )
VAR AppointmentCustomerGrouping66 = 
    FILTER(
        ALL('Table'),
        'Table'[Appt_type] = 66 && 'Table'[Customer] = CurrentCustomer
    )
VAR StartDate = 
    CALCULATE(
        MIN('Table'[Date]),
        AppointmentCustomerGrouping64
    )
VAR EndDate = 
    CALCULATE(
        MAX('Table'[Date]),
        AppointmentCustomerGrouping66
    )
VAR DateDifference = 
    DATEDIFF(StartDate,EndDate,DAY)
VAR Type66 = 
    IF(MAX('Table'[Appt_type]) = 66, DateDifference, 0)
RETURN
Type66

The problem is this shows the first date for a customer of appt type 64 and compares to the last date for that same customer in appt 66. Your table seems to show you have some other way to group data. For example, you are showing that for customer 12345 at the bottom that type 64 is Dec 31, 2019, and type 66 is Jan 6, 2020. Which is 7 days, not 9. Not sure where 9 comes from.

But the first date for customer 1234 of type 64 isn't Dec 31, 2019, it is Feb 1, 2019, thus the result my measure returns of 339 days.