First, ignore all the already matched positions, they don't affect the answer at all. For the unmatched positions, there are three basic cases (already given in the examples):

("xx", "yy") => 1 swap, ("xy", "yx") => 2 swaps

So the strategy is, apply case 1 as much as possible, then apply case 2 if the last two unmatched are in this case, or fall into impossible if only one pair of unmatched left. This can be done via a simple math.