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x\left(x-2y\right)+6\left(x-2y\right)
Do the grouping x^{2}-2xy+6x-12y=\left(x^{2}-2xy\right)+\left(6x-12y\right), and factor out x in the first and 6 in the second group.
\left(x-2y\right)\left(x+6\right)
Factor out common term x-2y by using distributive property.