Question 293160
It would be 24 if there were no restrictions
For each in first position there are 6 ways 4*3*2*1
(abcd)  bacd    cabd   (dabc)
abdc    badc    cadb   (dacb)
(acbd) (bcad)  (cbda)  dbac
acdb   (bcda)  (cbad)  (dbca)
(adbc)  bdac    cdab   dcab
(adcb)  bdca    cdba   (dcba)
With the restriction we have 2+4+4+2=12
Brad and Cathy can't be next to each other.
All combos of bc and cb are eliminated
Either in 1st and 2nd position
bcad bcda
cbad cbda
either in 2nd and 3rd
abcd dbca
acbd dcba
either in 3rd and 4th
adbc dabc
adcb dacb
That removes 12 leaving 12