Looks like you have a router, not just a modem. 10.240.151.128 is an IP assigned to the PC on your private/local network on your side of the router. The router has its own public IP on the internet side. If you want to ping the router from some other connection you need to know that public IP. The simplest way to get that is to browse to www.whatismyip.com from a PC on your local network. Many routers have a configuration option to not respond to a ping, but if it does allow ping you should be able to ping it using that IP from other PC’s connected to the internet. The router routes traffic from the public IP to and from the local IP’s of the connected PC’s using “Network Address Translation” (NAT).
I suggest you search on “Router”, “Network Address Translation” or “NAT”, and “Port Forwarding” to get a better understanding of how the internet and your network are working.