Try this in C6 and filled down.

=COUNTIFS('Attendance Records'!$B:$B,Overview!$B6,'Attendance Records'!$G:$G,Overview!C$5,'Attendance Records'!C:C,">="&C$3,'Attendance Records'!C:C,"<="&C$4)

The problem you're going to have is when you fill it to the right.
Your dates in row 3 and 4 are Merged Cells
Take C3:D3, those are merged and show 22-June
The problem is that only C3 actually contains the date, D3 is actually blank.
You'll have to manually adjust the formula to refer to the date in the left cell of each date range.