The Hidden Quadruplet is of course the logical extension of the Hidden Triplet . However, the Hidden Quadruplet is considered a very difficult higher method.
We're looking for a group of four candidates which are distributed over a total of exactly four fields within a logical unit. Each of the fields must contain at least two candidates of the group and may additionally have other random candidates. But no candidate of the group can occur outside of the fields of the Quadruplet.
If the criteria are fulfilled, then these four fields must ultimately be filled in with these four candidates. Right now we do not yet know how exactly the candidates will be distributed. What we do know, however, is that any additional candidates - that is, those which do not belong to the Quadruplet group - can be eliminated from the fields of the Quadruplet.
Does this sound familiar? It should, because basically this principle of thought started with the basic method Hidden One.
There isn't a realistic example for this method, because in 9x9 puzzles it is extremely rare that a situation arises in which all easier methods fail and a Hidden Quadruplet is suddenly the best option for further progress.
If you want to see an example of a Hidden Quadruplet, there is one here in the Hexadoku section. With larger the dimensions of a puzzle, the higher the probability is for this pattern.
see also: Generalization: Hidden groups