How to move taskbar to different monitor on Linux Mint?

To move it to a different monitor, right click on an empty area, select "Properties" and then uncheck the 'Expand' box. Now left click on the end one of the ends and drag it to a different monitor. Right click again on the end (making sure not to hit any other widget in the panel) and click on Expand again.

The panel appears on the primary monitor. You have not said how you are setting your system up so I can't give you a very detailed answer. You will need to use xrandr to find out you current setup. In my case this is:

$ xrandr | grep -w connected
VGA-0 connected 1440x900+1600+0 (normal left inverted right x axis y axis) 408mm x 255mm
DP-3 connected 1600x900+0+0 (normal left inverted right x axis y axis) 344mm x 194mm

So, DP-3 is my laptop's screen and VGA-0 is my external VGA monitor. Since I want the panel to be on the VGA which is extending the desktop to the right of the laptop, I would run:

$ xrandr --output VGA-0 --mode 1440x900 --primary --right-of DP-3 \
   --output DP-3 --mode 1600x900

The --primary switch sets the VGA screen as the primary monitor and causes the panel to be displayed on it.

For Mate, this worked for me: right click on the existing panel and click on "new panel" (it's near the middle). A new panel will appear (usually at the top). Now right click on the new panel and unclick expand. Move it the secondary monitory, and then select expand again.

Now right click on the new panel. Search for window list and add it. You may want to resize it, lock it and move it to your liking. You now have the open windows on each monitor on their respective panel.