$$ \frac{48xy^3}{12x} : \frac{8y^2}{6x^2} = \frac{48xy^3}{12x} \cdot \frac{6x^2}{8y^2} = \frac{48xy^3 \cdot 6x^2}{12x \cdot 8y^2} = \frac{288x^3y^3}{96xy^2} = 3x^2y $$
Ответ: $$3x^2y$$