I recently installed Cygwin-X on my Windows 10 laptop.  Problem was Putty with X11 forwarding was not working.  It took some Google and trial and error, but the following needed to be done.  Hope this helps you out:

For Cygwin-X:

• Edit the script that starts XWin Server
• (right-click on the shortcut in the Start Menu, select More > Open File Location, right-click on XWin Server and select Properties)
• Add the addition in Red to the Target

  C:\cygwin64\bin\run.exe --quote /usr/bin/bash.exe -l -c "cd; exec /usr/bin/startxwin -- -multiwindow -listen tcp"

For Putty:

• Under the X11 section, browse for the xauthority file located in your Cygwin home directory
• Select it and save the profile