In a Local Area Network machine A can ping to Machine B. But machine B is not able to ping to machine A!! What could be the possibilities?

Firewall on Machine A, the only possibility i know of.

The problem is caused by MachineA firewall. Well most of the time you hv to "penetrate into the firewall and allow inbound connection for the port" ordinarily you can just off the Pc firewall or the antivirus firewall but it's not a recommended solution.