The value of $$\left(18 \div 2 of \frac{1}{4}\right) \times \left(\frac{2}{3} \div \frac{3}{4} \times \frac{5}{8}\right) \div \left(\frac{2}{3} \div \frac{3}{4} of \frac{3}{4}\right)$$ is:

$$\left(18 \div 2 of \frac{1}{4}\right) \times \left(\frac{2}{3} \div \frac{3}{4} \times \frac{5}{8}\right) \div \left(\frac{2}{3} \div \frac{3}{4} of \frac{3}{4}\right)$$

= $$\left(18 \div  \frac{1}{2}\right) \times \left(\frac{2}{3} \div \frac{3}{4} \times \frac{5}{8}\right) \div \left(\frac{2}{3} \div \frac{9}{16} \right)$$

= $$36 \times \left(\frac{2}{3} \times \frac{4}{3} \times \frac{5}{8}\right) \div \left(\frac{2}{3} \times \frac{16}{9} \right)$$

= $$36 \times \frac{5}{9}\div \frac{32}{27} $$

= $$36 \times \frac{5}{9}\times \frac{27}{32} $$ 

= $$9 \times \frac{5}{9}\times \frac{27}{8} $$ =135/8

= $$16 \frac{7}{8}$$