Perhaps one way ..
Assuming you have in col A, A1 down
July 2004 Daily Numbers
July 2004 Weekly Numbers
August 2004 Daily Numbers
August 2004 Weekly Numbers
September 2004 Daily Numbers
September 2004 Weekly Numbers
etc
Put in B1:
=MID(TRIM(A1),SEARCH(" ",TRIM(A1),SEARCH(" ",TRIM(A1))+1)+1,99)
Copy down
Col B will extract the text-string after the "Month Year" string
Use col B as the key to sort both cols A and B
Alternatively,
Try Data > Text to columns to split col A into 4 columns:
In Step1: Ensure/Check "Delimited"
In Step2: Check "Space"
Click Finish
(Note: Ensure you have 3 empty cols to the right of col A first)
Use col C as the key to sort all the cols A to D