"We like bread with the soup."
Translation:Wir mögen Brot zu der Suppe.
"Wir möchten" means "We'd like to have", so indeed you can say that to a waiter if you want to order some bread with your soup, but "We'd like to have" has a different meaning from "We like". The second is a general remark that you enjoy it, it's not mentioning that you would like to get something. Next to that it should be "zu" and not "mit", see wataya's comment earier.