I'm not sure you can move just one pinned icon to the right side, however to move all to the right side do this:
Right-click on Desktop and select New Folder (Don't worry about its name, just let the default name stay)
Right-click on Taskbar and if Lock the taskbar is checked, click it to remove the check; i.e. unlock taskbar
Right-click the Taskbar again; this time select Toolbars > New toolbar
Choose the New Folder you just created and click the Select Folder button
Sample image of what you will now see
You can see your New Folder on the right side where you'd like your pinned icons to be.
Note the || lines. One pair is just to right of the Search icon. The other pair is just to the left of New Folder.
Move your mouse cursorover the two vertical lines [ || ] to left of New Folder to get a double arrow
When you see the double arrow left-click-and hold mouse button down, then drag all the way to the vertical lines located just to right of Search icon, then release left mouse button. The New folder will now locate there and your pinned icons will swap to the far right side.
Now right-click on the New Folder. You will see that Show text and Show title are both checked. If you click each of those items to remove check the New Folder will now be invisible on your taskbar.
Sample image of final result
If my instructions are a little difficult to follow, and you'd find it easier to see these steps in action, then take a look at this video that shows how its done:
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