Answer
True
Work Step by Step
We have $\{1,2,3,4\}$ has $4!=24$ distinct permutations. Interchanges of adjacent numbers result in alternating changes in the parity of the permutations, as we can see. Then we get one adjacent odd parity permutation for each even parity permutation. As a result, we have 12 even parity and 12 odd parity permutations.
