How many ways can 3 boys and 3 girls stand in a row so that the two girls are not next to each other?

I am assuming you mean "no two girls". Anyways, we see, that the only way for no girl to be together is if they sit BGBGBG or GBGBGB.

Therefore, we can do a premutation to see how many different ways this is possible. 

So:

2 * 3! * 3! = 72.