There is a pin conflict between the Ethernet Shield and Mux Shield II for pins 10, 11, and 12. However, you can use the Mux Shield II with the Ethernet Shield in a few different ways:
1. Use the solder jumpers on the back of the Mux Shield to hardwire the shield so that each row of 16 I/O connections are either inputs or outputs. See the User Guide section called “Freeing up Pins by Using Solder Jumpers”
2. Use the Go Between Shield between the Ethernet Shield and Mux Shield II to change the Mux Shield II conflicting lines (IOS1, IOS2, and IOS3) to any open lines on your Arduino.