|It won't work without a SOHO router between each subnet.|
You show the following NIC settings on one computer:
First network card
Second network card
This won't work since the gateway IP of each NIC is on a different subnet from the IP address. Without a route between the two subnets, they can't talk. This is why I said what I did in my very first sentence. This computer will not be able to communicate with anything if you set it up like this. You could probably add routes between the two subnets in the PC's routing table and make it work, I don't know, I wouldn't set anything up the way you suggest.
For info on adding another router (or more than one) to an existing network, click on my name above and read my "how-to" guide titled, "◦Add a second Router to your LAN" Pay attention to the scenario where you connect "WAN port to LAN port" for details on connecting multiple subnets.
It's worth noting, if you don't have a specific reason for going with multiple subnets, you really shouldn't bother (keeping the KISS principle in mind).
If you do require multiple subnets, I'd consider spending some money on a better router that has enough interfaces to support the number of subnets you require. An enterprise level, L3 switch could work too.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.