Thank you for your post.
FileMaker Pro 8.5 was the first version to be certified with Leopard (10.5.x). FileMaker Pro 9 and FileMaker Pro 10 seem to both work properly under Snow Leopard.
Although FileMaker Pro 6 is an older product, try uninstalling and reinstalling FileMaker Pro 6 on Snow Leopard. See if you are able to then turn on Web Sharing. If not, make sure you are using Snow Leopard 10.6.1 which came out recently. This fixed a number of minor problems, but it is unknown if this works with FileMaker Pro 6. If it doesn't, then your option is to either reinstall Leopard or upgrade FileMaker to FileMaker Pro 10.