So if you want it as a simplified fraction, when dividing fractions you use the rule:
1) keep the first fraction the same so 4/9,
2) change the divide to a multiply, 4/9 x
3) flip 8/15 to become 15/8
Then your final question will look like this:
4/9 x 15/8
Then you do 4x15 (numerator multiplied by numerator) to get 60 on the top
Then do 9x8 which is 72
So your answer is 60/72
But, this is not simplified, there is a common factor of 12 in both the numerator and denominator.
So you divide 60 by 12 and get 5
Then divide 72 by 12 and get 6
Therefore, your final answer is 5/6. Hope that helps :)