Instructions
Approach the other survivor with the vines in your inventory and speak to him. He will tell you to put the vines in the workshop in order for him to work with it.
Walk up to the basket near the firewood stockpile in your cave. Press the "A" button when your character is standing directly in front of the basket. The word "Check" will display at the bottom of your screen to indicate you are in the right position.
Press "Up" on the D-pad to deposit the vines in the basket. It is the "workshop" that the other character jokingly refers to.
Speak to the other character again and select the option for her to make a rope. Tell her she has two days to do it in; if you placed the vines correctly in the "workshop," she will get started.