There will be $4$ different necklaces.
- When $2$ black beads are separated by $4$ white beads or $2$ white beads.
- When $2$ black beads are adjacent.
- When $2$ black beads are separated by $1$ white beads or $5$ white beads.
- When $2$ black beads are separated by $3$ white beads.
$\color{purple}{\text{This is in a circular permutation.}}$
So,$\color{green}{\text{ there are 4 different necklaces we can form out of 2 black beads & 6 white beads.}}$