In general it is not possible for a web site that you access to learn your MAC address. However there are special cases where the server could learn your MAC address:
1. IPv6 supports assigning addresses in a way which embed the MAC address in the IP address. For privacy reasons this way of assigning IPv6 addresses is not very common.
2. If you are directly attached to the same network segment as the web server, it will be able to see your MAC address. (But this is probably not the scenario you had in mind.)
3. I have seen some ISPs embed the MAC address of the customer's equipment in reverse DNS records (the format was `x1-6-` followed by the MAC address).
4. There might be scripting capabilities in the browser which would allow scripts to learn the MAC address of the client machine and send it to the server. I do not know whether javascript can acquire the MAC address of the client machine, but I know that it can find the local IP address.