Step 1 :Given the math problem $4 / 9 \times 3 / 8$.
Step 2 :First, divide 4 by 9.
Step 3 :Then, divide 3 by 8.
Step 4 :Finally, multiply the two results together.
Step 5 :The final result of the operation $4 / 9 \times 3 / 8$ is \(\boxed{0.16666666666666666}\).