How to force Incognito Mode on Google Chrome
This will force Google Chrome to launch on Incognito mode
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On Admin Mode, go to Start and search for "regedit" and Open Registry Editor.

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Go to Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Policies

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Right Click "Policies" and Create a new Key named "Google"

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Once "Google" has been created, create another new key named "Chrome"

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Go to the Chrome folder (Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Google\Chrome)
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On the right side, right click and Create a "DWORD (32 bit value)

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Once it has been created, right click on it and click "Modify".

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Set the the Value Data to "2" and click ok

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Right Click on the Created DWORD again and rename it to "IncognitoModeAvailability"

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Check these entries and it should look like this when you're done.

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Restart the PC.