Assuming that any letter entered in a cell is an absence that should be counted try the following array entered formula:
Formula:
=SUM(IF(FREQUENCY(IF((B4:NC4<>"")*(B$2:NC$2>=EDATE(TODAY(),-6))*(B$2:NC$2<=TODAY()),COLUMN(B4:NC4)),IF((B4:NC4="")*(B$2:NC$2>=EDATE(TODAY(),-6))*(B$2:NC$2<=TODAY()),COLUMN(B4:NC4))),1))
Let us know if you have any questions.
Edit: If on the other hand you only want to count certain letters such as S, L and HD then try:
Formula:
=SUM(IF(FREQUENCY(IF(((B4:NC4=NQ$5)+(B4:NC4=NQ$6)+(B4:NC4=NQ$7))*(B$2:NC$2>=EDATE(TODAY(),-6))*(B$2:NC$2<=TODAY()),COLUMN(B4:NC4)),IF((B4:NC4="")*(B$2:NC$2>=EDATE(TODAY(),-6))*(B$2:NC$2<=TODAY()),COLUMN(B4:NC4))),1))
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