Решение:
$$6b^3c^2 \cdot \frac{c^2}{5b^4} = \frac{6b^3c^2 \cdot c^2}{5b^4} = \frac{6b^3c^4}{5b^4} = \frac{6c^4}{5b}$$
Ответ: $$\frac{6c^4}{5b}$$