I built the application in 32 bit RHEL 6.3 machine. I would need to deploy in RHEL 6.3 64 bit RHEL 6.3 X86_64 bit server machine.

when I browse I have learned that X86_64 will not contain 32 bit system libraries by default. I am wondering is this correct? because windows , solaris , hp all contains 32 bit libraries as well by default to be compatible with 32 bit applications though the it is 64 bit OS. Linker will identify the appropriate one to link.

Please clarify Running 32 bit applications in RHEL 6.3 X86_64 is different?

the most simple thing you can do is: just try it. You are right, usually the 32bit libs not installed, and if they were missing you need to install them. (and if you will make a package you can specify dependencies accordingly)