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