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y^{2}\left(6y-7\right)-2\left(6y-7\right)
Do the grouping 6y^{3}-7y^{2}-12y+14=\left(6y^{3}-7y^{2}\right)+\left(-12y+14\right), and factor out y^{2} in the first and -2 in the second group.
\left(6y-7\right)\left(y^{2}-2\right)
Factor out common term 6y-7 by using distributive property. Polynomial y^{2}-2 is not factored since it does not have any rational roots.