As you probably know by now, Windows 8 comes with what is being called Modern Apps, that are completely different from
Previously baptized Metro Apps, this special type of programs does not come with the standard “x” button that allows users to close them, so an early adopter may have quite a hard time to quit such an app. In fact, it’s a matter of time until you discover all Windows 8’s secrets, but that’s actually the purpose of this tutorial.
There are four different ways to close a Modern App, but they also depend on the platform you’re running Windows 8 on.
First of all, the Alt + F4 keyboard shortcut still works. Obviously, this is only available if you’ve installed Windows 8 on a desktop computer or on a laptop because it requires a keyboard.
The only problem is that this hotkey works exclusively if the target app is currently active on the screen, just like in the traditional “desktop” mode. So open the Modern App you want to close, press Alt + F4 and you’re done.
Another way to quickly quit a Modern App is to launch the Task Manager. That’s right, the Windows 8 Task Manager displays all running Modern Apps and give you the power to close them individually. Again, you need a keyboard to quickly launch the Task Manager (the hotkey is Ctrl + Shift + Esc). Simply select the app you wish to close, hit the “End Task” option and that’s it.
Tablet users on the other hand can quit these apps by simply dragging them down to the bottom of the screen. There’s nothing too complicated, so simply tap drag the top of the app to the bottom of the screen and it gets automatically closed. The same works for desktop computers too, with the only difference being that you have to use your mouse.
The last and the most used Modern App closing method is the one that requires a mouse action. In case you have already switched to desktop mode and you’re not working with the Modern App anymore, move your mouse to the top left corner and wait for a second. A taskbar showing all running Modern Apps shall appear, so you need to right click its thumbnail and hit the “Close” option.
Via: How to Close Windows 8 Modern (Metro) Apps