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\frac{3xy-6yz-x+2z}{4}
Factor out \frac{1}{4}.
3y\left(x-2z\right)-\left(x-2z\right)
Consider 3xy-6yz-x+2z. Do the grouping 3xy-6yz-x+2z=\left(3xy-6yz\right)+\left(-x+2z\right), and factor out 3y in the first and -1 in the second group.
\left(x-2z\right)\left(3y-1\right)
Factor out common term x-2z by using distributive property.
\frac{\left(x-2z\right)\left(3y-1\right)}{4}
Rewrite the complete factored expression.