Multiway Cut question
The analysis of the approximation algorithm (join all min-cuts between a terminal and the contraction of the remaining terminals, excluding the heaviest cut) starts on slide 13. So there's nothing to compute, simply assume that $A^*$ is the optimal solution with cuts $A_i^*$ separating terminal $i$ from the rest of the graph. To see the argument spelled out more explicitly read e.g. chapter 4 of Vazirani's "Approximation Algorithms".