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.
