Ok, so what you do is to first realize that you may order the boys in $8!$ ways. Hopefully you already know how to reason here. (You may choose the first one in $8$ ways, the second in $7$ ways, and so on.)
The same reasoning goes for the girls, here we get $7!$ ways to sit them down.
Now for each order of boys, $8!$, you may order the girls in $7!$ ways, so by the rule of product you can sit them down in $8!7!$ ways.
Now, think of all boys/girls, sitting down in a row, as one group, call the groups $B$ for boys and $G$ for girls (you have $8!$ such boy groups, and $7!$ such girl groups). Then you have to take into account that you may order these two groups in $2!$ ways, namely $BG$ and $GB$. (This is because you couldn't mix the two groups up, because of the condition of boys/girls sitting contiguously by gender. You may only mix up the order of the groups.)
Again then, by rule of product, you have $8!7!2!$ ways in total.