Answer
They should tie the cord to a pole and both boys should pull together on the opposite end.
Work Step by Step
Let's assume that each boy can pull on the cord with the same force $F$.
First let's tie the cord to a pole and let one boy pull on the cord with a force of $F$. Then the tension in the rope is $F$. Note that the pole also exerts a force of $F$ on the rope, pulling in the opposite direction from the boy.
If we replace the pole with one boy, so then one boy is pulling at either end of the cord with a force of $F$, the situation is essentially the same. The tension in the rope is still $F$.
Let's tie the cord to the pole and let both boys pull from the same end of the cord. Then the force on the cord is $2F$, the tension in the cord is $2F$, and the pole exerts a force of $2F$ on the cord in the opposite direction from the two boys. Since the tension in the cord in this situation is $2F$, clearly this method has a better chance of breaking the cord.
They should tie the cord to a pole and both boys should pull together on the opposite end.
