The most common and most likely answer to this crossword clue is the 3 plus 2 plus 1 plus 4 plus 2 plus 3 letter word PUT IN A WORD OR TWO
I've seen this crossword clue in The Times
P
U
T
I
N
A
W
O
R
D
O
R
T
W
O
Buddy explains!
The straight part
We know that "Make favourable mention of" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make favourable mention of = put in a word or two.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.