Please help solve this riddle: "When two persons shake hands with one another, in how many ways it is possible--20, 25, 40, or 45?"

I would love to help you with this question, but I just
can't seem to make sense out of it.  I think you've worded the question incorrectly?
 Two people meet each-other, right?  How many ways can two people shake
hands? Unless you are talking about secret handshakes and such, of which
there would be an infinite number, I can't see a total of more than 3 ways that make
sense: right to right/left to left, are both hands at once.   But that's only 3 ways,
not anywhere near 20, 25, 40, or 45...

If it is not a
comfortable handshake, you could do r/r r/l l/l l/r and all 4 at once, but even that is
just 5.

It has the making of a joke and not a true math
puzzle.  I would suspect some kind of punch-line if you hadn't given only 4 possible
answers.