The answer is
1/6
For this kind of question, we cannot just simply split the terms as every term is connected to each other.
Therefore, the logic is
multiplication
Here is the process:
(3/2)*(2/3)=1
(2/3)*(3/4)=1/2
(3/4)*(1/3)=1/4
(1/3)*(3/8)=1/8
(3/8)*(1/6)=1/16
Hope this clarifies.