To solve this problem, we first need to convert all the mixed numbers to improper fractions:

3/8 1 5/7 4/9 2 1/3
= 3/8 12/7 4/9 7/3
= 36/56 48/63 28/9
= 9/14 16/21 28/9
= 2/2 16/7 28/9
= 16/7 * 28/9
= 448/63
= 64/9

Therefore, 3/8 1 5/7 4/9 * 2 1/3 = 64/9