Two identical pies were cut into a total of $16$ equal pieces

Each pie was cut into $8$ pieces

If one piece was cut into $3$ pieces what fraction of a pie did each person receive?

Since one pie was cut into $8$ equal pieces and one piece was equally distributed among three peoples, each person got $1$ out of $8 \times 3 = 24$ pieces

So the answer is $\frac{1}{24}$

Choice B is the answer.