Hungarian Algorithm - Bipartite Graph Approach
(Converting a comment into a proper answer. Note that I now use the minimum cost convention of the reference given in the question.)

Any augmenting path serves. Note that you reverse the order of the arcs. Say you choose AW of cost -2 first. Then you have forward arcs AX, BW, BX, and backward arc WA, which has been reversed. Now BW,WA,AX is an augmenting path, of cost -6+2-2=-6, and you end up with backward arcs WB,XA which represent the optimal solution 8.