Step 1 :This problem is a classic example of a permutation problem in combinatorics. Sally has to visit each of the 8 cities once and only once, and then return to her home city. This is equivalent to finding the number of permutations of 8 distinct objects, which is given by 8!. However, since she can start her journey from any of the 8 cities, we need to multiply this by 8 to get the total number of ways she can inspect all cities and return home.
Step 2 :Calculate the total number of ways as \(8 \times 8!\)
Step 3 :The total number of ways is \(322560\)
Step 4 :Final Answer: \(\boxed{322560}\)