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