When new there was a tag on it which might still be there.
If it is an MTD box it will have a code number cast into the casing.
Then there is the way it works.
If it has actual gears like a car with a reverse position then you need grease.
If it has a foot pedal for speed control and another lever for F-N-R
Then it may need liquid grease if it has a diff only
or 20W 50 synthetic if it is a full hydro.
Some photos would be of great help. particularly of the speed controller.
