When you browse C:\Windows\System32 in XYplorer on 64-bit Windows you see a file listing that differs from the one you would see using Windows Explorer. The reason for this is Microsoft's WOW64 Redirection, which helps making 32-bit applications work on 64-bit Windows. Quoting Microsoft:
The %windir%\System32 directory is reserved for 64-bit applications. Most DLL file names were not changed when 64-bit versions of the DLLs were created, so 32-bit versions of the DLLs are stored in a different directory. WOW64 hides this difference using a file system redirector. In most cases, whenever a 32-bit application attempts to access %windir%\System32, the access is redirected to %windir%\SysWOW64. Access to %windir%\lastgood\system32 is redirected to %windir%\lastgood\SysWOW64. Access to %windir%\regedit.exe is redirected to %windir%\SysWOW64\regedit.exe.
This means when XYplorer lists C:\Windows\System32 you actually see the contents of C:\Windows\SysWOW64. There are several ways to work around this.
Disabling file system redirection is possible but not supported by XYplorer (unless by a tweak). This solution is not recommended because it can result in unexpected behavior, e.g. missing confirmation prompts in file operations!
The recommended solution is using the Sysnative alias for System32. Again quoting Microsoft:
32-bit applications can access the native system directory by substituting %windir%\Sysnative for %windir%\System32. WOW64 recognizes Sysnative as a special alias used to indicate that the file system should not redirect the access. This mechanism is flexible and easy to use, therefore, it is the recommended mechanism to bypass file system redirection. Note that 64-bit applications cannot use the Sysnative alias as it is a virtual directory not a real one.
These are the redirections invoked by WOW64 for 32-bit applications on 64-bit Windows:
C:\Windows\System32 ---> C:\Windows\SysWOW64
C:\Windows\Sysnative ---> C:\Windows\System32
So if you need to access C:\Windows\System32 you specifiy C:\Windows\Sysnative instead. In order to do this you have to manually create an empty folder C:\Windows\Sysnative (resp. %windir%\Sysnative) once using Windows Explorer 64-bit.