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