【Analysis】This problem examines permutations and combinations.
【Solution】Solution: Starting from one face, there are 4 different directions to choose from for the first move. The number of cases for these four directions is the same, so we only need to consider one, let's consider the case of starting from the front,
$$
\begin{array}{l}
\text { Front } \rightarrow \text { Top } \rightarrow \text { Back } \rightarrow \text { Right } \rightarrow \text { Bottom } \rightarrow \text { Left } \rightarrow \text { Front } \\
\text { Front } \rightarrow \text { Top } \rightarrow \text { Back } \rightarrow \text { Left } \rightarrow \text { Bottom } \rightarrow \text { Right } \rightarrow \text { Front } \\
\text { Front } \rightarrow \text { Top } \rightarrow \text { Left } \rightarrow \text { Bottom } \rightarrow \text { Back } \rightarrow \text { Right } \rightarrow \text { Front } \\
\text { Front } \rightarrow \text { Top } \rightarrow \text { Left } \rightarrow \text { Back } \rightarrow \text { Right } \rightarrow \text { Bottom } \rightarrow \text { Front } \\
\text { Front } \rightarrow \text { Top } \rightarrow \text { Left } \rightarrow \text { Back } \rightarrow \text { Bottom } \rightarrow \text { Right } \rightarrow \text { Front } \\
\text { Front } \rightarrow \text { Top } \rightarrow \text { Right } \rightarrow \text { Bottom } \rightarrow \text { Back } \rightarrow \text { Left } \rightarrow \text { Front } \\
\text { Front } \rightarrow \text { Top } \rightarrow \text { Right } \rightarrow \text { Back } \rightarrow \text { Left } \rightarrow \text { Bottom } \rightarrow \text { Front } \\
\text { Front } \rightarrow \text { Top } \rightarrow \text { Right } \rightarrow \text { Back } \rightarrow \text { Bottom } \rightarrow \text { Left } \rightarrow \text { Front }
\end{array}
$$

Therefore, the total number is $4 \times 8=32$ (ways).
Hence, the answer is: 32.
10. (10 points) An ant starts from the center of one face of a cube, and each time it moves to the center of an adjacent face, visiting each center exactly once, and finally returns to the starting point. The total number of sequences of centers visited is $\qquad$. (Two sequences are different if the order of centers visited along the path is different)