\[\boxed{\mathbf{359}\mathbf{.}}\]
\[1)\ \frac{5}{12}x = \frac{1}{6}\]
\[x = \frac{1}{6}\ :\frac{5}{12}\]
\[x = \frac{1}{6} \cdot \frac{12}{5}\]
\[x = \frac{2}{5}.\]
\[2)\ \frac{7}{16}\ :x = \frac{3}{4}\]
\[x = \frac{7}{16}\ :\frac{3}{4}\]
\[x = \frac{7}{16} \cdot \frac{4}{3}\]
\[x = \frac{7 \cdot 1}{4 \cdot 3}\]
\[x = \frac{7}{12}.\]
\[3)\ \frac{13}{17}x = 39\]
\[x = 39\ :\frac{13}{17}\]
\[x = 39 \cdot \frac{17}{13}\]
\[x = 3 \cdot 17\]
\[x = 51.\]
\[4)\ x\ :\frac{8}{27} = 18\]
\[x = 18 \cdot \frac{8}{27}\]
\[x = \frac{2 \cdot 8}{3} = \frac{16}{3}\]
\[x = 5\frac{1}{3}.\]