Why a server cannot ping other's private IP

so what could be the problem and how can it be solved.

Your firewall is not configured correctly on the node not replying to ping.

-- sw

Thanks for the reply. Sorry I omitted one thing, there is a dev server with a private IP which can ping Server A and vice verse.

simple Illustration
Server A -- Can ping B and C
Server B -- Cannot Ping A and C
Server C -- Can ping A and B

Thanks

Server B -- Cannot Ping A and C

This is the one with the misconfigured firewall. It's blocking ICMP Echo requests.

-- sw

ufw is not active. This is a fresh server that has been deployed

You can have an active firewall without ufw…and you can have firewall rules that ufw doesn’t/can’t manage.

This is because ufw is not the firewall. It’s only a friendly front-end™ to the real firewall to make it easy for you to use. It’s pretty easy to go behind ufws back. Sometimes that’s the only way…

Also, you need to make sure the private IP is even configured on Server B… See:

https://www.linode.com/docs/guides/managing-ip-addresses/#adding-private-ip-addresses

Try putting A's & C's private IP addresses in B's /etc/hosts file:

192.168.xxx.xxy                   server-a
192.168.xxx.xxz                   server-c

Since addresses the private IP address range are not in any kind of DNS system and their traffic is not routable to other networks, this is the only way you can make them known to other systems in the same data center.

— sw