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4y\left(x-3\right)-3\left(x-3\right)
Do the grouping 4xy-12y-3x+9=\left(4xy-12y\right)+\left(-3x+9\right), and factor out 4y in the first and -3 in the second group.
\left(x-3\right)\left(4y-3\right)
Factor out common term x-3 by using distributive property.