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3xy\left(2y-1\right)+4\left(2y-1\right)
Do the grouping 6xy^{2}-3xy+8y-4=\left(6xy^{2}-3xy\right)+\left(8y-4\right), and factor out 3xy in the first and 4 in the second group.
\left(2y-1\right)\left(3xy+4\right)
Factor out common term 2y-1 by using distributive property.