Answer
This graph has 479,001,600 Hamilton circuits.
Work Step by Step
This complete graph has 13 vertices. We know that the number of Hamilton circuits in a complete graph with $n$ vertices is $(n-1)!$.
The number of Hamilton circuits in this graph is $(13-1)!$ which is $12!$. Since $12! = 479,001,600$, this graph has 479,001,600 Hamilton circuits.