In the troubleshooting section of the shop manual for "Mower does not move forward..." section, here's the list:
Drive clutch lever freeplay excessive (adjust cable)
Lever or cable damaged (replace cable)
Drive belt worn or damaged (replace belt)
Drive belt came off (inspect pulleys)
(Internal) Transmission malfunction (replace trans.)
Shift cable out of adjustment (adjust cable)
Shift cable damaged (replace cable)
You need to verify both the shift cable and clutch cable are fully moving the control arms on the top of the transmission. If not, check freeplay, loose connections, stretched cable(s), etc. If all these don't help, it is likely an internal fault inside the transmission. There are no service parts for it, and it must be replaced as a unit. The part number is
20001-VH7-001, list price $109.97.
Google any part number to find a Honda Dealer selling it online, or use this link to find a Honda Dealer in your area:
Find A Honda Dealer
You may find a paper copy of the shop manual helpful, especially if you decide to R&R (remove and replace) the transmission. Honda sells paper copies on Amazon and eBay, free shipping and free updates for 3 years.
Honda Power Equipment Shop Manuals on eBay
Honda Power Equipment Shop Manuals on Amazon