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4b\left(b-6\right)-3a\left(b-6\right)
Do the grouping 4b^{2}-24b-3ab+18a=\left(4b^{2}-24b\right)+\left(-3ab+18a\right), and factor out 4b in the first and -3a in the second group.
\left(b-6\right)\left(4b-3a\right)
Factor out common term b-6 by using distributive property.