I'm not sure I understand your question.
Asphyre has nothing to do with pathfinding. Asphyre is a framework that makes game development easier, but there's nothing in there AFAIK that does any game logic.
The algorithm used in your screenshot is the common A* algorithm. Google 'A*' and you'll find plenty of explanations and implementations of the A* algorithm.
When you have implemented the A* algorithm you can easily use Asphyre (or some other framework/drawing method) to draw the result of your algorithm.