Factor the Greatest Common Factor.

12y^3 + 27y^2

Both terms have a common factor of 3y^2.

12y^3 / (3y^2) = 4y
27y^2 / (3y^2) = 9

Therefore, the greatest common factor of 12y^3 + 27y^2 is 3y^2(4y + 9).