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