Counting how many date ranges have dates that fall within another date range

Hi, JFarq 

Please try formula like:

calculated column:

Absence Occurences per person per month  =
CALCULATE (
    COUNT ( Absence_Data2[Start Date] ),
    ALLEXCEPT (
        Absence_Data2,
        Absence_Data2[Start Date].[Month],
        Absence_Data2[Start Date].[Year],
        Absence_Data2[Forename And Surname]
    )
)

Measure:

count of absence date =
CALCULATE (
    COUNTROWS ( Absence_Data2 ),
    FILTER (
        Absence_Data2,
        Absence_Data2[Start Date] >= MAX ( 'Calendar (UK?)'[StartOfMonth] )
            && Absence_Data2[Start Date] <= MAX ( 'Calendar (UK?)'[EndOfMonth] )
    )
) + 0

(need change the data type of 'Calendar (UK?)'[StartOfMonth], 'Calendar (UK?)'[EndOfMonth] from 'Text' to 'Date')

Best Regards,
Community Support Team _ Eason