Why can't I quit Finder with the shortcut (cmd+q)
Finder isn’t like a regular application. It has to be running to manage certain things. I forget exactly what all the things are but I think it includes the desktop icons. Because of this Apple made it so you can’t use CMD + Q to quit the application.

To close a Finder Window

The shortcut to close a finder window(so like when you open a folder) is CMD + W

To relaunch Finder

If finder stops responding you can relaunch it by going into Force Quit and relaunching it. The force quit menu is accessed by clicking on the Apple in the top left and then clicking force quit, then you select finder and click relaunch.

Quit Finder by using terminal

If you do actually need to quit finder you can do so by running a terminal command.
Run the command:

killall Finder


Adding the Quit option to Finder

As it says at this answer,
Running the command defaults write com.apple.finder QuitMenuItem -bool YES &amp;&amp; killall Finder will give the Quit option and will allow the shortcut CMD+Q