\[\begin{array}{l}
c)\frac{3}{4}:\frac{4}{5}:\frac{5}{6} = \frac{3}{4} \times \frac{5}{4} \times \frac{6}{5} = \frac{{18}}{{16}} = \frac{9}{8}\\
2)\\
a)2 \times \frac{3}{8} \times 4 \times \frac{2}{9} = \frac{{2 \times 3 \times 4 \times 2}}{{2 \times 4 \times 3 \times 3}} = \frac{2}{3}\\
b)\frac{2}{3} \times \frac{4}{5} + \frac{1}{3} \times \frac{4}{5} = \frac{4}{5} \times \left( {\frac{2}{3} + \frac{1}{3}} \right) = \frac{4}{5} \times \frac{3}{3} = \frac{4}{5}\\
c)\frac{1}{6} \times \frac{4}{{11}} + \frac{3}{4} \times \frac{4}{{11}} = \frac{4}{{11}} \times \left( {\frac{1}{6} + \frac{3}{4}} \right) = \frac{4}{{11}} \times \frac{{11}}{{12}} = \frac{1}{3}\\
d)\left( {1 + \frac{1}{2}} \right) \times \left( {1 + \frac{1}{3}} \right) \times \left( {1 + \frac{1}{4}} \right) \times \left( {1 + \frac{1}{5}} \right)\\
= \frac{3}{2} \times \frac{4}{3} \times \frac{5}{4} \times \frac{6}{5}\\
= \frac{6}{2}\\
= 3
\end{array}\]