Try this:

=SUMPRODUCT(--($C$7:$C$450=X7), --($B$7:$B$450<=AC3), --($B$7:$B$450>=Z3), --($G$7:$G$450=Z6), $M$7:$M$450)


That should work, if it doesn't, you're probably having a "matching" error with the dates, perhaps caused by formatting issue that AC3 and Z3 aren't the same format as you column B dates.