Using a Switch and P2P transfers (Very bad MS Paint inside)

[Gimpymoo]

If for example, setup is like this...

(My art degree is in the post)

If a file is sent from Computer A to Computer B, does the transfer go:

Computer A> Switch> Router> Switch> Computer B

Or does it go:

Computer A> Switch> Computer B?

Hope that makes sense.

I know switches are not "Dumb" but not sure how smart they are either.

Thanks.