Question 883539
There are 6 beads in that necklace and each one is a different color.
Identify the colors by the codes 1, 2, 3, 4, 5, and 6.
Lay the necklace on the table and look for the bead of color 6.
What are the other colors read clockwise from that bead?
Is it 12345? 15324? Some other sequence
There are {{{5!=5*4*3*2=120}}} such sequences.
 
However, {{{12345}}} and {{{54321}}} represent the same necklace flipped over.
By laying the necklace on the table we made it easier to count the possibilities, but we counted each one twice.
There are {{{120/2=highlight(60)}}} possible necklaces.
 
NOTE:
Your teacher wants you to mention "permutations".
It is just one of many names/words (hopefully not too many) that they will make you learn. Words and symbols help us communicate more efficiently, as long as we use them just as necessary.