Jasmine has 4 glass ornanents: green, orange, brown, and purple. how many ways can she hang them in a row so that the green and brown ornaments are not next to each other.

The best way to solve this is by giving a visual idea of the glass ornaments. so We will have letter G represent Green, O for Orange, B for Brown, P for Purple.
Sample 1:G,O,B,P
Sample 2:G,P,O,B
Sample 3:P,G,O,B
Sample 4:O,G,P,B
Sample 5:G,O,P,B
This is what you can do this should be the right amount of ways to arrange them.

1:green,purple, brown, orange
2:purple, green, orange brown
3:green, orange, brown purple
4:brown, orange, green, purple

The first one is correct