Replacing 3-way swtich on 4-way Circuit Issue

[Hillyard]

I'm having a bit of an issue where I thought I took a picture but it didn't save and now I'm not sure how two of my light switches were wired.

These are the wires in the double ******** box.
Mudroom Light - Single Pole Light Switch
Red
White
Black - Hot

Garage Light - 3-way Light Switch (4-way circuit)
Red
White
Black (Powered off Mudroom Light, White becomes hot - tested by multimeter)

The mud room light has black and red at the light fixture.

The 3-way switch for the garage shares the hot wire (black) from mud room light. When I connect the black wires, the white wire on the 3-way switch becomes hot too.

I've googled diagrams but nothing shows up similar to my situation or maybe I'm not wrapping my head around it correctly.

 

[walta]

Do you have something like this?

Walta

 

[Jim greengo]

Do you have something like this?

Walta

 

[matt_i]

Why do they nut the black to white conductors and then land both black and white conductors on the lamp......such a nice diagram there otherwise.

As a basic concept to keep in mind for future circuits and troubleshooting the chain has to start and end with 3 ways, you can have any number of 4 ways in the between the ends.

 

[Bert_]

Why do they nut the black to white conductors and then land both black and white conductors on the lamp......such a nice diagram there otherwise.

That's the way I do it. Make the white hot all the time so it can't be confused with a neutral.

 

[Hillyard]

I really appreciate the help, the first single pole switch having three wires was really causing me some confusion. I think it all makes sense now though, hopefully.

Does this seem right?
First switch
Black
Red
(White not connected)

Second switch
Black is shared to power first switch
White is hot and coded (Which wasn't originally)
Red
(Black not connected) connected to (White not Connected) to complete the neutral.