6. $$ \frac{12m^2}{17c^4} : \frac{6m^4}{35c^3} $$

$$\frac{12m^2}{17c^4} : \frac{6m^4}{35c^3} = \frac{12m^2}{17c^4} \cdot \frac{35c^3}{6m^4} = \frac{12 \cdot 35 \cdot m^2 \cdot c^3}{17 \cdot 6 \cdot c^4 \cdot m^4} = \frac{420m^2c^3}{102c^4m^4} = \frac{70}{17} \cdot \frac{1}{c} \cdot \frac{1}{m^2} = \frac{70}{17cm^2}$$