Question 1193982
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B = boy
G = girl


The back row must alternate in gender. 
We could have BGBG or GBGB
Either way, all the boys are in the back since there are only 2 boys on the team.


Case BGBG:
There are 2 ways to arrange the boys in this configuration (for slots 1 and 3) 
For the girls in the back row, we have 4 ways to fill the second slot and 4-1 = 3 ways to fill the fourth slot. That gives 4*3 = 12 ways to select the girls for the back row.
So far we have 2*12 = 24 ways to form the back row in the configuration of BGBG.
Then for the front row, we have 2 ways to arrange the remaining girls to go on either side of the coach.
In all, there are 2*24 = 48 ways to arrange all divers such that we have the format BGBG in the back row.


Case GBGB:
As you can probably guess, not much is different here compared to the previous case above. We have the same basic values to deal with.
There are 2 ways to arrange the boys, 4*3 = 12 ways to select the girls in the back row, and 2 ways to arrange the remaining girls up front. So we have 2*12*2 = 48 ways to form case GBGB.



In short, we found 48 ways to have the format BGBG in the back row. And we also found 48 ways to have GBGB in the back row.


Therefore, we have 2*48 = 96 different configurations overall.


Side note: order matters when it comes to problems like this when we arrange people in a photograph.
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