I think I can address your confusion without "working the problem for you".
Why do we make the assumption that the centripetal force is equal to the weight of the block at the top of the arc (i.e. position B in your diagram)? The reason is that when the centripetal force is equal to the weight at position B, this means that the pendulum has the minimum speed needed to just barely make it over the top of the loop. Any additional speed would result in the rope having tension, and any less speed would mean that the rope would go slack.
When assuming that the centripetal force was equal to the weight at position B, it follows that the bullet had the minimum speed to get the pendulum over the loop, and so forth.
The "minimum speed to get something to loop-over something else" occurs frequently in first semester physics.