You do know by default, when customer logout, the cart will be empty right? the cart items will be back only when customer re-login. I assume you just want to save an empty cart to the account when logout.
3 things you need to know before doing this task
1, module, model and object
you will use 2 module for this task: customer and checkout, in app/code/core/Mage, inside these 2 modules, there are customer model and cart model will help you
2, event and observer
there are all kinds of events in magento. when customer logout, magento will fire 'customer_logout' event, and you can register an observer to this event and clear cart
3, how to create your own module
http://magento.stackexchange.com/questions/41277/how-to-create-an-new-observer-on-the-event-catalog-...
alright, now in your custom module, register your observer, and that observer method should be
function clearCartBeforeLogout($observer)
{
Mage::getSingleton('checkout/cart')->truncate()->save();
}
be noted that if customer didn't click logout link, the cart won't be cleared.
