Well if I were to confirm that answer, I would have no way to know what you understand about this question.
Tell us what those numbers mean!
as per your suggestion;-
boys ways;-(7-1)=6!
now there are 5 girls and 7 seats(in b/w boys) so there are P(7,5) number of ways, the girls can sit.
p(7,5)=7!/(7-5)!
i.e, total no. of ways= 6!*p(7,5)
= 6!*7!/(7-5)!
= 1814400 (but this ans is wrong).
ans is = 252