TWD comes with the correct fmodex.dll in the install folder, which is Version 4.38.04.
The error message sounds like it's using a different version for some reason.
Please uninstall and reinstall TWD, to make sure you have the original files.
If it still doesn't work afterwards, we can try to find out which fmodex.dll the game loads.
For that
- Download and run
Dependency Walker.
- Open the file WalkingDead101.exe in Dependency Walker
- Click "Ok" if you get an error window
- In the table with the .dlls, click on the column name "Module" in order to sort the table by dll name
- Select fmodex.dll in the Module column. Pressing the F key should get you there quickly
- Press F9 to show the full path of the fmodex.dll
- Check if the path is the same as your TWD installation directory
- Scroll right until you see the "File Ver" Column
- Check if the Version is 0.4.38.4