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How to terminate skype from the task manager 
Right-click on the skype icon on your computer's taskbar. 
You should see a window including different options such as " quit skype, " " skype, " " pin the program, " and " close window. " 
Click on the quit skype tab in the window.
You should see a confirmation dialog box from skype stating that you will not be able to send or receive instant messages should you quit. Click on the " quit " button in the dialog box.