When you divide by a fraction all you have to is multiply by the reciprocal. The reciprocal of 3/8 is 8/3.
The real problem is 2/3 TIMES 8/3. Multiply the numerators across 2 X 8 = 16. Then multiply the denominators across 3 X 3 = 9. The answer is 16/9. If you need to simplify then the answer is 1 7/9.