You can do what you have suggested as long as you are aware that the Openreach modem will need to plugged into the Ethernet port that is next to it and that Ethernet port will need to be connected to the four port socket in the study.
You will then need to connect your Smarthub into the socket that came from the Openreach modem. This is your "master" broadband connection.
The other three ports of the four port socket will need to feed one port to each of the remaining rooms.
You would then be able to plug an Ethernet into one of the Smarthub's ports and then into one of the remaining ports on the four port socket. This will then allow the room that that port is connected to by the internal Ethernet cable to function. You then connect the next one in a similar manner.
This will however only work if your builder has or will run the internal Ethernet cable in the correct way. ie Ethernet socket next to the Openreach modem and terminated at socket terminal 1 at the fourway in the study.
Ethernet socket in room one run to study and terminated at four way socket terminal 2.
Ethernet socket in room two run to study and terminated at fourway terminal 3.
Ethernet socket in room three run to study and terminated at fourway terminal 4.
