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Hi Bob, My name is ***** ***** I would be happy to help before I answer your question I just want to clarify a few things and ask a couple of questions.
1. Does the 4-way switch have four screw terminals not including a green ground screw? (typically two silver and two brass)
Your red and white should be your travellers at each 3-way going on the screws that match in color. Your blacks should go on the common. There is a lot of different ways to wire a 3-way, 4-way combo so if that not your solution we may need to dig further. Please make sure you have the power off to the circuit before working on it. If you need help turning it off please let me know.
There should be one red and one white on the brass (from the same cable or conduit)
Sometimes just using colors to identify the function of a wire does not work because how it was originally wired may not be proper or standard. If you switch the travellers at the 4-way and it does not function properly then we will need to go into much more detail.
I am sorry if I was not clear...
Just switch one of the red and whites so you have on red and one white on the black screws. just verify that both wires on the black screws come from the same cable or conduit.