This is the number of derangements of 4 distinct objects:
[ !4 = 4!\left(1 - 1 + \dfrac12 - \dfrac16 + \dfrac1{24}\right) = 24\left(\dfrac12 - \dfrac16 + \dfrac1{24}\right) = 24\cdot\dfrac{12-4+1}{24} = 9. ]
(Alternatively: total permutations ( 4! = 24 ), subtract those with at least one fixed point using inclusion-exclusion yields 9.)
Answer: 9 ways