The value of $$54\div16  \text{of} 3\times[12\div4  \text{of} \left\{6\times3\div(11-2)\right\}]\div(12\div8\times2)$$ is:

$$54\div16  \text{of}  3\times[12\div4  \text{of}  \left\{6\times3\div(11-2)\right\}]\div(12\div8\times2)$$

= $$54\div16  \text{of}  3\times[12\div4  \text{of}  \left\{6\times3\div9\right\}]\div(\frac{12}{8}\times2)$$

= $$54\div16 \text{of} 3\times[12\div4  \text{of}  \left\{6\times\frac{3}{9}\right\}]\div3$$

= $$54\div16 \text{of} 3\times[12\div4  \text{of}  2]\div3$$

= $$54\div16  \text{of} 3\times[12\div8]\div3$$

= $$54\div16 \text{of}  3\times\frac{12}{8}\div3$$

= $$54\div48\times\frac{12}{8}\div3$$

= $$\frac{54}{48}\times\frac{12}{8\times3}$$

= $$\frac{9}{16}$$

Hence, the correct answer is Option D