I have a Honda self propelled lawnmower hrt216s3da that turns left but not right i took transmission out sanded shaft and replaced everything

SOURCE: Troy Bilt Self Propelled Lawnmower drive belt

belts usually come off for a few reasons.
They become loose...stretch or the tensioner moves,  Make sure that none of the tightening bolds are slipping.  You can dab them with a bit of paint.
when the pulleys are not in alignment or crooked or bent.  Eyeball the path from one pulley to another, also make sure the tensioner is in alignment and there are no other obstructions.
good, high quality belts are required, and they must be real drive belts...not regular v belts.  If there is a way to watch the belt in operation you can usually see what's going wrong.
On my lawnmower I had to grind some metal away where the belt went from the motor to the transmission.  Good luck 

SOURCE: Self propelled lawn mower inside of drive wheel gears stripped.

Check the drive shaft bearing closest to that wheel.

SOURCE: Self Propelled mower quit self propelling

you probaly have a broken gear or engagment lever. the part the cable goes through before the cable goes thru the deck. you also could have sheared a pin or the plastic gear that drives it.

SOURCE: Honda HRB 216 self propelled mower Cable Broke for self propelled

there is a panel in front of the gear that completes the curve of the blade path that you can remove with a single bolt on the outside of the mower between the wheel and the deck

SOURCE: Honda lawn mower, self propelled mechanism not working

check the mechanism first before changing the gearbox its possible that the cable might jump out from the pulley or the cable is worn out or its possible that the gear on the tire is worn out to if not then that would be the time for you to change the gear box it would be hard to change it if you don't have the right tools to work on it if you know how everything work its not that hard to replace it just make sure were everything goes memorize the parts before disassembling cause that would be you guide to reassemble it...goodluck