\[\left( 3\frac{5^{\backslash 3}}{12} - 2\frac{2^{\backslash 4}}{9} \right) \cdot \frac{12}{43} + 2\frac{2}{3} =\]
\[= \left( 3\frac{15}{36} - 2\frac{8}{36} \right) \cdot \frac{12}{43} + 2\frac{2}{3} =\]
\[= 1\frac{7}{36} \cdot \frac{12}{43} + 2\frac{2}{3} = \frac{43}{36} \cdot \frac{12}{43} + 2\frac{2}{3} =\]
\[= \frac{1}{3} + 2\frac{2}{3} = 2\frac{3}{3} = 3.\]