i have a 2007 buick lucerne 3.8 after extended driving on highway i get to my destination and park for about a 1/2 hour then i run to the store when i com out and start the car it stumbles and shuts off it only happens after a long trip

What happens if you slightly step on the gas pedal while starting it?

If you can, in the same situation open the hood for five minutes before starting. Does this help?

Also:

How many miles are on it?

How old is the battery?

What part of the world does this car live in?

Has it always lived there?

Also, if the hard start is only with a warm engine, check the vac line to the fuel pressure regulator for fuel...