Use the picture to answer these two questions.

identify two pairs of action-reaction forces involving the rope. is there motion?

use newton’s third law to explain what would happen if the rope suddenly slipped out of the white dog's mouth.

1. There is tension acting in the rope. The rope being pulled from the brown dog exerts tension force in the direction of the black dog and according to Newtons 3rd law the black dog would exert an equal and opposite force of tension in the rope towards the brown dog so there would be no motion at this point; 
2. The brown dog and the black dog would be pushed away from each other at equal force but in opposite direction according to Newtons 3rd law. 
This could also be related to Newtons 2nd law which is about resultant force and F=ma but since the question only asks for 3rd law its probably not appropriate.