The question describes a search method that starts exploring from a starting node. If it reaches a point where it cannot proceed further (a dead end), it goes back up the path it took (backtracks) to find an alternative route.
This behaviour is characteristic of Depth First Search (DFS). DFS explores as far as possible along each branch before backtracking.
Therefore, the search that begins at a starting node and backtracks upon hitting a dead end is a Depth First search.