The abbreviations of the 12 months of the year (each having 3 letters) as follows:
JAN, FEB, MAR, APR, MAY, JUN, JUL, AUG, SEP, OCT, NOV, DEC
Since the clue words have a total of 36 letters, and as per the hint, each abbreviation has the same number of letters, then the number of abbreviations/members in the group, which is more than 4 as per the hint, had to be one of:
6 x 6 letters each = 36 letters, or
9 x 4 letters each = 36 letters, or
12 x 3 letters each = 36 letters, or
18 x 2 letters each = 36 letters
since these (6, 9, 12, and 18) are the only remaining numbers that 36 divides evenly into.
So with the hint and a bit of logic, counting the total number of letters in the clue words helps to narrow down the number of possible answers substantially.