Tom - Mark,

Yesterday, when the <clothes> washer went into the spin cycles, gray water was blowing out of the stack.

The drain system had been cut into sections so I was able to disassemble the stack and found the blockage at the exit of the "P" trap.

I cleared the blockage and the washer works fine. However, there is now a gray water backup into the kitchen sink.

Any suggestions?

I assume you are talking about a clothes washer, right? Sounds like when you rodded out the line you also moved the clog downstream. Is there a clean out down stream of the sink trap, if so rod from there with a 1/4" snake. You will hit a 90 elbow about 5' into the wall and the 1/4" can make that bend. If you find a clean out then use a bigger rod.

Bob,

Okay, I'll see if I can find another clean-out. Right now the only one I can find is outside at the rear of the house.

Here is a sketch of the layout. The sink is about 6' from the rear wall of the kitchen where the clothes washer drain line is.

The washer's connection to the drain line may also be a place to insert a 1/2'or larger rod if you can fully open the connection and get in there. I am having difficulty getting my head around your sketch. The sink is in the dining room?

I'm a qualified horrible artist!

No the dining room is to the front of the galley style kitchen.

there is now a gray water backup into the kitchen sink. I think Bob nailed it when he sais;
Sounds like when you rodded out the line you also moved the clog downstream.
And now your blockage is dowstream from the kitchen sink. If you can't find a cleanout then rent a sewer machine and snake from the kitchen roof vent. Put out enough snake to reach the base and 20 feet more. Good luck, Tom