I have never seen a listing of Snapper models by year, but that does not mean the info does not exist.
On the Snapper rear-engine riders, the first two digits of the model number were the width of cut. .....Yours cuts a 28' swath.
The next two digits usually signified the hp of the engine. ....Yours was 8hp.
The 'S' in the model number signifies the mower came with an electric starter.
I don't know if the '6' has any special significance, or if it indicates the last digit of the year of manufacture. ......I would guess that your machine was built in the 1980's, so it is quite possibly a 1986 model, but I don't know that for certain.
Hopefully, someone else will be able to answer more precisely. ....I got out of the mower business in 1983, so I am not very familiar with the models made after that.
If you have a B&S engine, the first two digits of the CODE number are the year of engine manufacture. ....The next two digits indicate the month. ......Of course, if the engine is not original to the mower, that will not help date your Snapper.
If you have a Tecumseh engine, I believe the engine can also be dated by the serial number.
....A Google search should find the info you need to date them.