Start with Tom with Amy on his right. Since there are only three girls and both Bob and Hank wish to sit between two of them, one of these two must come next. Obviously it has to be Hank as otherwise he would be next to Gladys. After Hank there must be Eileen, followed by Bob and Gladys. Naturally, the remaining empty seat beween Gladys and Tom is occupied by Charlie, the complete order being
Tom-> Amy-> Hank-> Eileen-> Bob-> Gladys-> Charlie-> Tom (Tom's name is shown twice ti indixate the circular arrangement). It is evident that Charliesat down three places to Eileen's right.