3 way switch is one input and two possible outputs. When you flip the switch you chang to witch output is connected to. The other output will not be connected to anything.
A 4 way switch has two input and two out outs. Let call the input a and b and the output x and y.
The switch has to state one where a-x and b-y are connected. when you flip the switch you change it so a-y and b-x are connected.
So input is always connected to output the difference it witch output
Look at the wiki page illustrations that show the idea with two 3 ways and one 4 way. You could add any number of 4 ways in the middle and it would work the same.
[https://en.wikipedia.org/wiki/Multiway_switching#More_than_two_locations](https://en.wikipedia.org/wiki/Multiway_switching#More_than_two_locations)
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