I get 24. If you divide the guests into groups of 4, and have everyone in the group shake with everyone else in that group, you get 6:
A shakes with B,C, and D
B shakes with C and D
C shakes with D
Everyone has shaken with everyone in their group one time. Do the same thing in each of the 4 groups and you get 24.
There are other ways to set it up, but the answer SHOULD always be 24.
Hope this helps!
Matt in New York