“A Worn Path” is an example of which kind of archetypal story?

The most common archetype attributed to this story is the "journey" archetype.

Explanation:

Phoenix Jackson has a mission (quest) to accomplish something (get medicine for her grandson), follows a "path" she knows well, faces many difficulties along the way, and a journey that does things beyond just to get the medicine. What she learns along the way is part of the quest and it is what makes or does not make her successful.

1.the hosts on two opposing mountains stood,  

2.thick as the foliage of the waving wood;  

3.between them an extensive valley lay,  

4.o'er which the gleaming armour pour'd the day,  

5.when from the camp of the philistine foes,

6. dreadful to view, a mighty warrior rose; in the dire deeds of bleeding battle skill'd,

d is the best answer for this question.