If you ever find yourself in a position where multiple GPOs are linked to the same place and they are fighting each other for settings, it will probably be in your best long-term interests to revisit those GPO settings and edit them so that you can create harmony between all of the GPOs that are linked to a particular location. However, sometimes this is simply not possible, and so you may have to throw those GPOs into the boxing ring and let them duke it out.
Thankfully, changing the priority of GPOs is very easy. We do this from the same location we have been working in previously, inside GPMC's Linked Group Policy Objects tab. When multiple GPOs are listed here and you want to change the Link Order so that higher-numbered policies start taking precedence over lower-numbered policies, you simply choose the GPO that you want to re-prioritize and click on the up or down arrow buttons that are displayed along the left-hand side of the window.
In previous screenshots, you have seen that my Set Desktop Wallpaper to Orange 2 GPO is Link Order number 1, and is therefore the GPO setting that is being pushed into place on the client workstations that reside inside my Accounting OU. I now have the desire to make sure that my Set Desktop Wallpaper to Blue 1 GPO is the one who wins, and so I have clicked on that GPO and then simply clicked the up arrow button shown here:
You can see that the Blue 1 GPO now has Link Order number 1 priority, which means that this GPO is the one that is going to apply last on my workstations, and therefore be in place when I log in to LAPTOP1. Let's test it out. As with most changes inside GPMC, these link order adjustments take immediate effect, and so all I have to do is restart LAPTOP1, log in to it, and see that my wallpaper has changed: