#### Answer

The path A,B,C,D,G,F,E,A is a Hamilton circuit.
The path A,F,G,D,C,B,E,A is a Hamilton circuit.

#### Work Step by Step

A Hamilton path is a sequence of adjacent vertices that visits each vertex in the graph exactly once. A Hamilton circuit is a Hamilton path that begins and ends at the same vertex.
Let's start at vertex A. The path can travel to vertex B, then to vertex C, then to vertex D, then to vertex G, then to vertex F, then to vertex E, and then finally back to vertex A.
This path is A,B,C,D,G,F,E,A. Since this path visits every vertex in the graph exactly once, this path is a Hamilton path. Since this Hamilton path starts and ends at the same vertex, this path is a Hamilton circuit.
We can find another Hamilton circuit in this graph.
Let's start at vertex A. The path can travel to vertex F, then to vertex G, then to vertex D, then to vertex C, then to vertex B, then to vertex E, and then finally back to vertex A.
This path is A,F,G,D,C,B,E,A. Since this path visits every vertex in the graph exactly once, this path is a Hamilton path. Since this Hamilton path starts and ends at the same vertex, this path is a Hamilton circuit.