Ireally need betty has 6  grandchildren: jeni, sarah, rachel, kristen, lindsey, and carolyn. jeni, sarah, and rachel are sisters; kristen and carolyn are sisters; and lindsey is an only child if the sisters must sit together, how many different ways can the 6 grandchildren be seated at a circular table?

There are three groups of grandchildren. That is, 3 sisters, 2 sisters and 1 child.
Now,
Number of ways of all of them to sit = 3! = 6 ways
Numbers of ways in which three sisters can sit = 3! = 6 ways
Number of ways in which two sisters can sit = 2! = 4
Number of ways in which the child can sit = 1! = 1

Therefore,
Total number of ways in which the grandchildren can sit = 6*6*4*1 = 144 ways.