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Now, you're correct that often when you perform a 'pop' you return the value of the node being popped. However in this case it is actually more useful to pop the entire linked-list node off the top of the list, because the goal is to end up with the same number of items in the final list, so you can save having to delete and re-create any, but simply changing what the nodes point to, and what points to them. In this manner, you end up simply reordering the nodes in the list themselves.
I didn't understand the goal of this paragraph.