To walk the Shih Tzu (commonly pronounced Shit Zu) is a slang term, used to denote the act of human defecation. Shih Zu being a breed of dog, originating in Asia, having to walk the shit zu does not refer, in this context, to providing one's pet dog with exercise, but in fact the impending urge of a human to defecate.

When you eat dirt for the first time and leave your family to build a shack in the woods