How to I find my key number?

What kind of boat is it and are you talking door or ignition? (I keep 911-915 door keys on a ring because their pretty common.) Trial and error is your best bet that I know of, or just pick up a new cylinder or ignition. If an ignition key that may be your only option or a good lock smith. Also, are you absolutely sure there are no keys on board. Most owners hide a set for in case they forget to bring their home set.
Also, the manufacturer will probably have a record of the key numbers depending how old the boat is.

I believe that's a Southco lock. Common. Check whatever dealer you're closest to (pretty much any make) and try a bunch starting with the 911 to 915 once you have the number just order one. If your marina doesn't have a set of keys remove the lock and bring it to someone who does or simply order a new cylinder. If you're locked out and can't borrow keys to try, pick the lock. (Even the wrong key can often be manipulated if it fits) Boat doors are not very secure. (Mis-spent youth) P.S. these keys are cheap. Ignition keys are often a different matter so protect them (one set hidden on the boat and one set home).
Some of the newer Carvers have a different type of lock which is more secure. If that's you case contact the factory with your boat ID #. Most locksmiths today simply break or drill the locks causing you to replace. So if you call one in make sure they're experienced, reputable and can pick a lock.

Is this a Mobella lock? Most 466's I have seen have the Mobella lock with very few southco's but they are out there.

Im not really sure about the boat or the lock,
but once a broke my last key to my salon door.

i removed the cylindar and brought it to a locksmith.
the locksmith made me a bunch of keys for $25.

in the future, i will try not to break off my last key in the lock.