I think the question asks for a count of rows where the date is before AY12 and the other columns are blank (not populated). It's simpler to "nest" the IF statements, I think - I'd use this version
=ARRAYFORMULA(SUM(if(Mona!$C$4:$C$400<=$AY12,if(Mona!$B$4:$B$400="",if(Mona!$D$4:$D$400="",if(Mona!$E$4:$E$400="",1))))))
Note that blank cells in column C will also be deemed to be <=AY12 so if those might be blank too then you might want to add a check to ensure that that column is not blank, i.e.
=ARRAYFORMULA(SUM(if(Mona!$C$4:$C$400<=$AY12,if(Mona!$C$4:$C$400<>"",if(Mona!$B$4:$B$400="",if(Mona!$D$4:$D$400="",if(Mona!$E$4:$E$400="",1)))))))
Replace commas with semi-colons if your version requires it
Note that your COUNTIF formula quoted above doesn't need the "Arrayformula" part, can simply be this
=COUNTIF(Mona!$F$4:$F$400;"<="&$AY12)
Best Answer
There are many ways to do this. Try this one:
=counta(iferror(filter(B2:B, B2:B = today())))
The benefit of this pattern is that you can easily add more conditions to the
filter()
.