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Currently my network has 2 routers - Router A and Router B.
Both router are connected to a modem.
Both router has different public ip address and default gateway.
Router A | IP-123.123.123.123 | Gateway-192.168.0.100
Router B | TP-456.456.456.456 | Gateway-192.168.0.199
Printer A is connected to Router A, what I need to do in order to allow user in Router B to be able to connect to and using the Printer A?
Thank you
If this is in fact a single network with two separate gateways, then the fact that there are two separate gateways should be irrelevant with properly-functioning equipment as long as all devices attempting to use the printer are connected to the same LAN and are using the same IP addressing scheme (e.g. 192.169.0.x). The internal/LAN ports of each router should act as switches, and each router should see the other router as a network switch, allowing traffic to move through. This assumes that there is a network connection between the LAN sides of the two routers.
If there are in fact two separate networks both using the same IP addressing scheme, each with its own router and a VPN between them, then you aren't going to be able to do this without changing the addressing on one side or attempting some more advanced techniques to change the network sizes. In fact, it's unlikely that any router would allow such a VPN connection to be established unless it was using a very unusual network stack (most are based on a limited number of original source implementations).
If you are using Network Address Translation (NAT), then you'll need to enable a way for connections from Router B to pass through Router A and be directed to Printer A's internal IP. The simplest way to do this is to forward all unsolicited traffic to Router A's IP to Printer B's internal IP (this is usually possible on most home routers). The caveat, and it is a big one, is that Printer A is visible to the Internet, and therefore can be hacked and used to get inside your internal network.
If you want a more secure solution, you'll either need a router with at least two internal-facing network ports or a second router to create a new internal LAN isolated from your existing network. The printer is still exposed, but can no longer compromise your existing internal LAN. Here's a quick overview of how this works at a conceptual level (https://en.wikipedia.org/wiki/DMZ_%28computing%29)
What you need is a Site-to-Site VPN between your networks. Depending on what router you have, they may support VPNs. Otherwise, you'd need a machine or appliance to manage those VPNs on both networks.
If your use is personal or for a small business, you might want to consider a solution such as Google Cloud Print.
