I recommend that you draw a wiring diagram prior to purchasing and installing product.
The attached line drawing shows my intentions for a three room installation. The first room to start is where you'd find both an Ethernet and coax drop in the home, which is in the home office for this project. I have starred (*) wherever I am adding equipment or cables that was not there previously.
The following steps will explain the room by room installations.
Generally speaking, I am adding a coax splitter to each room. One outbound port will go to the cable set top box (STB) while the other port will go to the coax adapter. The coax adapter is then connected by an Ethernet cable to the respective connected devices.