I can't trace that part number through Kohler spare parts - I think that is the number of a carburetor part, not a carburetor. Usually the only parts serviced are wearing bits such as gaskets/seals, floats, needles, perhaps butterfly pivot shafts, maybe jets. Otherwise you replace the whole carburetor. I've looked through the carburetor service parts list, and there is nothing beginning with 6. Hence I do not think you can replace the part that belongs to that part number. You might or might not be able to get a complete carburetor, if we can trace the engine model and if it isn't too old for parts still to be available.
Can you photograph the leak so we can talk about what part is actually damaged?
Meanwhile, here is the Kohler carburetor service manual, in case you can find the carburetor from the pictures. That cross-links to engine model numbers:
http://www.kohler-engine-parts.opeengines.com/flash/Carburetor_Parts_Reference_Manual.swf
