The most common and most likely answer to this crossword clue is the 3 plus 2 plus 3 plus 2 letter word HOW DO YOU DO
I've seen this crossword clue in The Daily Telegraph
H
O
W
D
O
Y
O
U
D
O
More clues leading to the result HOW DO YOU DO
Buddy explains!
The straight part
We know that "form of greeting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case form of greeting = how do you do.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.