\[3\frac{4^{\backslash 2}}{9} - 2\frac{1^{\backslash 3}}{6} = 3\frac{4 \cdot 2}{18} - 2\frac{1 \cdot 3}{18} =\]
\[= 3\frac{8}{18} - 2\frac{3}{18} = 1\frac{5}{18}\text{.\ }\]