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a\left(x+2y\right)-4b\left(x+2y\right)
Do the grouping 2ay-4bx-8by+ax=\left(ax+2ay\right)+\left(-4bx-8by\right), and factor out a in the first and -4b in the second group.
\left(x+2y\right)\left(a-4b\right)
Factor out common term x+2y by using distributive property.