The most common and most likely answer to this crossword clue is the 4 letter word JUNE
I've seen this crossword clue in The Guardian
J
U
N
E
More clues leading to the result JUNE
- Judge with a Parisienne for thirty days
- In Strasbourg I must accept one follower of May
- Juliet getting French article for another girl
- Jack meets a French girl when Wimbledon starts
- Jack put on feminine Parisian article for some time
- … of twelve from US capital without a university
- Plane detailed to carry peacekeepers for a month
Buddy explains!

The straight part
We know that "6 (clue number) th of twelve (months)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case 6 (clue number) th of twelve (months) = june.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.