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So most of the articles say to add –newprivatetab to the arguments. However, newprivatetab does not work anymore.
It seems that the command line argument has changed in the newer versions of Opera.
How to launch Opera in Private Mode from Windows Shortcut
Find the Windows start menu shortcut (usually at C:\ProgramData\Microsoft\Windows\Start Menu\Programs) and go to its properties.
--private after the string
"C:\Program Files (x86)\Opera\launcher.exe" --private