$$\frac{3}{14}:3\frac{1}{7}=k:3\frac{2}{3}$$
$$\frac{3}{14}:\frac{22}{7}=k:\frac{11}{3}$$
$$\frac{3}{14}\cdot \frac{7}{22}=k:\frac{11}{3}$$
$$\frac{3}{44}=k:\frac{11}{3}$$
$$k=\frac{3}{44}\cdot \frac{11}{3}$$
$$k=\frac{1}{4}$$
Ответ:$$\frac{1}{4}$$