The reason that the number disappears when you change NM1 to =TODAY() is that today's date is 12/19/2019 and the dates of the absences in the file are between 12/10/2020 and 12/19/2020, so they are not in the past six months, but rather in the future.
If you want the formula to reference "s":
1. Select cell NM1
2. Select the Name Box which is window furthest to the left of the formula bar
3. Type s into the name box window and press the Enter key
4. Modify the formula to read: =SUMPRODUCT(COUNTIFS(B4:ND4,NL$5:NL$10,B$2:ND$2,">="&EDATE(s,-6),B$2:ND$2,"<="&s))
Let us know if you have any questions.