What is the quarter of quarter of half?

Given:
quarter$=\frac{1}{4}$

half$=\frac{1}{2}$

To calculate:
quarter of quarter of half

Calculations:

quarter of quarter can be calculated as $=\frac{1}{4}\times \frac{1}{4}=\frac{1}{16}$

quarter of quarter of half can be calculated as $$\begin{gathered} =\frac{1}{2}\times \left(quarter of quarter\right) \\ =\frac{1}{2}\times \frac{1}{16}=\frac{1}{32} \end{gathered}$$

Hence, the correct answer is Option B.