Factor the gcf: 12x3y + 6x2y2 − 9xy3.
3x2y(4x2 + 2xy − 3)
3xy(4x + 2xy − 3y2)
3xy(4x2 + 2xy − 3y2)
3x2y(4x3y − 2x2y2 − 3xy3)

To answer the problem above, determine the GCF of the terms. For the numerical coefficients 12, 6, and 9, the GCF is 3. For the x^3, x^2, and x the GCF is x. Lastly, for y, y^2 and y^3, the GCF is y. Thus, the GCF of the terms is 3xy. Divide each of the terms with the GCF. The division will lead to the factors: 
 
                                        3xy(4x^2 + 2xy - 3y^2)

Thus the answer is the third choice.