There are $4$ Boys & $4$ Girls
Criteria given is "All the Boys & Girls will be seat in a row" & "No two girls will be seat together"
I'll make Boys seat first in the row.
So, Boys can be seat in $4$ seats in $4!$ ways.
Now, there are $5$ seats left vacant.
Now, from these $5$ vacant seats, we could choose $4$ seats & make Girls seat.
& This can be done in $^5C_4 \times 4!$ or we can say $^5P_4$ ways
[ Why $^5C_4 \times 4!$ $ \rightarrow$ $^5C_4$ because we'll choose $4$ vacant seats out of $5$ seats & $4!$ because after choosing $4$ seats, we can arrange them in $4$! ways And $^5C_4 \times 4!$ can be written as$^5P_4$ ]
∴ Total number of ways will be = $4! \times ^5C_4 \times 4! $
$\qquad \qquad \qquad \qquad \qquad \qquad =4! \times ^5P_4 $
$\qquad \qquad \qquad \qquad \qquad \qquad = 24 \times 120$
$\qquad \qquad \qquad \qquad \qquad \qquad = 2880$