【Analysis】The insect travels from $A$ to $B$. At the first hexagon's fork, there are 2 paths both above and below. The hexagon where $B$ is located also has 2 paths both above and below. Therefore, there are $2 \times 2 + 2 \times 2 = 8$ paths. There are 2 paths for the arrow pointing back in the middle, making a total of 10 paths.

【Solution】Solution: The insect travels from $A$ to $B$. At the first hexagon's fork, there are 2 paths both above and below. The hexagon where $B$ is located also has 2 paths both above and below. Therefore, there are $2 \times 2 + 2 \times 2 = 8$ paths. There are 2 paths for the arrow pointing back in the middle, making a total of 10 paths.

Answer: The insect has 10 different routes from $A$ to $B$.
9. (10 points) A small insect crawls from $A$ to $B$ along the route shown in the figure. It is stipulated: the edges marked with arrows can only be traveled in the direction of the arrow, and each edge can be passed through at most once in the same route. How many different routes are there for the insect to travel from $A$ to $B$?



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