Jasmine had 4 bulbs: green, orange, brown, purple. How many ways can hang so green and brown are not next to each other

There are 4! ways in which she can hang the bulbs, which means 4x3x2x1. this is 24 ways.

g o b p

g o p b

g b p o

g b o p

g p o b

g p b o

o g b p

o g p b

o p g b

o p b g

o b p g

o b g p

b o g p

b o p g

b p o g

b p g o

b g o p

b g p o

p g o b

p g b o

p b o g

p b g o

p o b g

p o g b

of these ways, there are 12 where green and brown aren't next to each other