What style of deck do you have? I have seen both left and right discharge on the older round nose decks but i havent saw any of the newer decks like is posted above. As for the reason for the difference, i dont know myself but i noticed that most of the left discharge decks have a plate over the hole because i best guess is it blew all the grass onto the engine while mowing.
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Go to antiquetractors.com. and under garden tractor photos type in snappin turtle. The first one listed is greg in ohio and his is a left discharge. Then derek in ohio that is my collection 5 yrs ago before i sold some and added some.