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2a\left(y-4z\right)+3x\left(y-4z\right)
Do the grouping 2ay-8az+3xy-12xz=\left(2ay-8az\right)+\left(3xy-12xz\right), and factor out 2a in the first and 3x in the second group.
\left(y-4z\right)\left(2a+3x\right)
Factor out common term y-4z by using distributive property.