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2a\left(a+4b\right)-3\left(a+4b\right)
Do the grouping 2a^{2}+8ab-3a-12b=\left(2a^{2}+8ab\right)+\left(-3a-12b\right), and factor out 2a in the first and -3 in the second group.
\left(a+4b\right)\left(2a-3\right)
Factor out common term a+4b by using distributive property.