how do I close the Print Cener app on iPhone X?

I do know that on any iOS device that I have ever owned, the Print Center app closes on its own if I am not printing. I don’t have the X but I believe that you can also swipe up on the preview of the app to close it. Did you try swiping up

Have you tried restarting or force your restarting your phone?

On an iPhone X, iPhone 8, or iPhone 8 Plus: Press and quickly release the Volume Up button. Press and quickly release the Volume Down button. Then, press and hold the Side button until you see the Apple logo.

To close a running instance of the Print Center app on an iPhone X, swipe up from the bottom of your screen and pause. This will show you a list of running apps. Swipe from left to right until you find the app you want to close and then press for a few seconds on the screen until red ➖ signs appear by each app. Select the ➖ sign that appears at the top of the app that you want to close. More information on using your iPhone X can be found with this support article as well as with the iPhone and iOS 11 User Guide.

First I would try restarting your iPhone using the side button. Then, if that does not work, I would try deleting and reinstalling the Print Center app itself. You can do this from the home screen by pressing and holding on the particular app you want to remove (note-do not use a 'hard' press to activate 3D Touch). The apps should start vibrating and an ✖ (not red) will appear by each one. Click the X for the Print Center app and confirm.

Have you already tried to restart your iPX?

Regards

Giulio