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3x^{2}\left(x-2y^{2}\right)+y\left(x-2y^{2}\right)
Do the grouping 3x^{3}-2y^{3}-6x^{2}y^{2}+xy=\left(3x^{3}-6x^{2}y^{2}\right)+\left(xy-2y^{3}\right), and factor out 3x^{2} in the first and y in the second group.
\left(x-2y^{2}\right)\left(3x^{2}+y\right)
Factor out common term x-2y^{2} by using distributive property.