[tex]\displaystyle \Bigg[4+6\frac{2}{3} -\frac{9}{4} \cdot \left(\frac{1}{3}+\frac{1}{9}\right)\Bigg]:4\frac{5}{6} -2=\\ \\ =\left(4+\frac{6\cdot 3+2}{3} -\frac{9}{4} \cdot \frac{3+1}{9} \right):\frac{4\cdot6+5}{6} -2=\\ \\ =\left(4+\frac{20}{3} -\frac{9}{4} \cdot \frac{4}{9} \right):\frac{29}{6} -2=\left(4+\frac{20}{3} -1\right):\frac{29}{6} -2=\\ \\ =\frac{12+20-3}{3} :\frac{29}{6} -2=\frac{29}{3} :\frac{29}{6} -2=\frac{29}{3} \cdot \frac{6}{29} -2=\frac{6}{3} -2=2-2=\mathbf{0}[/tex]
