#### Answer

Using the Nearest Neighbor Method, the Hamilton circuit is C,D,B,A,C. The total weight of the circuit is 82.

#### Work Step by Step

With the Nearest Neighbor Method, we should choose the edge which has the smallest weight for each step along the path.
Let's start at vertex C. We can travel along edge CA, CB, or CD. The weight of these paths are 20, 24, and 10 respectively. We should travel along the edge CD because it has the smallest weight.
From vertex D, we can travel along edge DA or DB. The weights of these paths are 14 and 12 respectively. We should travel along edge DB because it has the smallest weight.
From vertex B, the path must travel to vertex A, and then finally back to vertex C to complete the Hamilton circuit.
Using the Nearest Neighbor Method, the Hamilton circuit is C,D,B,A,C. The edges in this path are CD, DB, BA, and AC. The weights of these edges are 10, 12, 40, and 20.
We can find the total weight of this Hamilton circuit.
total weight = 10 + 12 + 40 + 20
total weight = 82
Using the Nearest Neighbor Method, the Hamilton circuit is C,D,B,A,C. The total weight of the circuit is 82.