I have a WHITE / MTD ride on that looks just like your mower except for the colour of it.
Mine is a twin cylinder 12.5HP Briggs with 7 speeds.
I rebuilt the MTD transaxle in mine as it was a bit noisy.
I replaced some worn bushes and repacked it in grease. It's now running a lot better.
The transaxle in mine is only one gear forward and reverse.
You actually get the 7 speeds with the variable speed pulley set up.
Maybe your belt is worn and may need replacing.