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