8/24 is the answer
Let’s draw a picture to figure that out.
Let’s make a rectangle and split it into eight pieces since we are finding 8/9 of 3/8. Next, we will circle 3/8 because that is what we are diving up. Then we split the 3/8 into nine pieces since we are diving by 8/9. Then we will have one more group of three to split into nine pieces, so let’s do that. Then, since 9 divided by 3 is 3, we will split the last two pieces into 3 pieces each. Then we will shade in 8/9 of the circled pieces. Count all the pieces now, which should be 24 pieces. Then how many of those are shaded? 8/24 is the answer.