My approach to this problem was as follows - Seat all the boys in a row before the girls. Then arrange the 6 girls in the 7 places between the boys(5 places between the boys and 2 places at the extremes). Therefore, the answer will come out to be $6! * 7!$ .
What is written in the solutions - Seat all the 6 girls before the boys in a row. Now find the number of ways of seating 6 boys in the 5 places between the girls. For the one boy left, the number of places to sit in is 12. Therefore, the answer comes out to be $6! * 6! * 12$. What is the cause of these two conflicting answers? Is my approach wrong or is the approach given in the book wrong?