#### Answer

The path would need to use the edge connecting vertex D and vertex E twice and this is not permitted according to the definition. Therefore, A,C,D,E,D is not a path.

#### Work Step by Step

A path is a sequence of adjacent vertices. Two vertices are adjacent if there is an edge which connects the two vertices. Note that a path may not make use of the same edge twice.
From vertex A, a path can go to vertex C, then to vertex D, and then to vertex E. However, the path can not go back to vertex D because the path would need to use the edge connecting vertex D and vertex E a second time, which is not permitted according to the definition.
Therefore, A,C,D,E,D is not a path.