6. \(\frac{3}{4}:\frac{5}{6}+2\frac{1}{5}*\frac{2}{5}-1:\frac{1}{6}\)

\[\frac{3}{4}:\frac{5}{6}+2\frac{1}{5}\cdot\frac{2}{5}-1:\frac{1}{6}=\frac{3}{4}\cdot\frac{6}{5}+\frac{11}{5}\cdot\frac{2}{5}-6\]

\[=\frac{9}{10}+\frac{22}{25}-6=\frac{45+44-300}{50}=-\frac{211}{50}\]

Ответ: \(-\frac{211}{50}\).