After Arthur instructs Sheldon not to order the reuben, Sheldon tells him that he needs help with a problem in his marriage to Amy.
He says that there are two rules of marriage: don’t go to bed angry, and if you don’t recognize the shoes under your bed then they’re not yours.
He knows he’s upset her, but he tells Arthur that he doesn’t know how to make it right.
Sheldon is completely confused by the second rule, assuming that the shoes must be Amy’s if he doesn’t recognize them, but Arthur tells him to just forget that and stick with the first rule.