#### Answer

When Lancelot is 9.84 meters from the castle end of the bridge, the tension in the cable is at its maximum and it will break.

#### Work Step by Step

Let $L$ be Lancelot's distance from the castle end of the bridge. Let's assume that the tension $T$ in the cable is at its maximum. We can find Lancelot's position when the net torque about the castle end of the bridge is zero.
$\sum \tau = 0$
$(600~kg)(g)~L+(200~kg)(g)(6.0~m) - (5.80\times 10^3~N)(12.0~m) = 0$
$(600~kg)(g)~L = (5.80\times 10^3~N)(12.0~m) -(200~kg)(g)(6.0~m)$
$L = \frac{(5.80\times 10^3~N)(12.0~m) -(200~kg)(9.80~m/s^2)(6.0~m)}{(600~kg)(9.80~m/s^2)}$
$L = 9.84~m$
When Lancelot is 9.84 meters from the castle end of the bridge, the tension in the cable is at its maximum and it will break.