This example is one method of setting up a secure VNC session tunneling over SSH. It assumes a VNC server has been installed on the remote system.
Download and unzip MobaXterm Home Edition (portable edition)
Open MobaXterm and start local terminal
SSH into the remote system
#!/bin/sh
[ -x /etc/vnc/xstartup ] && exec /etc/vnc/xstartup
[ -r $HOME/.Xresources ] && xrdb $HOME/.Xresources
vncconfig -iconic &
dbus-launch --exit-with-session gnome-session &
After the vncserver is running, now can configure the vnc session in mobaxterm
Select VNC and enter localhost in the remote hostname and select the port the vncserver was started on like 5902 in the set above
Select SSH gateway (jump host) under the Network settings
In the SSH jump host enter the server name ase-tanaka-lab-1.ae.utexas.edu and your logon name
When you connect (execute) the session, it will first ask for your server password, the ask for the vncpasswd your set when configuring the vnc server session