UNIX for Advanced & Expert Users

I would like to know if there is a way to see what a user is doing from another terminal.

I want to be able to see exactly what they see on their terminal.

Is that possible ?

Im running Red Hat Linux 6.2

try the w command

Try a 'tty' to see the terminal number.

Then cat /dev/tty0 > tty0.log

'cat tty0.log' or 'more tty0.log'

Or try 'cat ~user/.history' or 'more ~user/.history'.

The default shell in Redhat has been bash for as long as I've used it.
The history will be found in /home/username/.bash_history by default. One thing that bash does, though, is saves the command history in memory, not writing to the .bash_history file until the user ends that session.
Redhat (probably, other Linux variants have it as well) does have a few good monitoring utilities available, though. Check the man page on "ttysnoop", and man "vcs". You can get a screenshot of a terminal by simply using cat. For example:
cat /dev/vcs0 > /root/tty0_log
more /root/tty0_log