To solve this use permutation or counting principle. The beads are ordered in a different arrangement each time to arrive at a unique necklace.
You need to consider the Red and the Black as one bead, since she decided that they stay next to each other.
You also have to consider that the order of the Red and the Black :
- Red-Black 4P4= 24
- Black-Red 4P4= 24
There are 48 different necklaces: 24 + 24 = 48
I think this is helpful.