$$3xy\times2+\frac{8x^{2}y^{3}}{2y^{2}}$$
$2xy\left(2x+3\right)$
$$factor(6xy+\frac{8x^{2}y^{3}}{2y^{2}})$$
$$factor(6xy+4yx^{2})$$
$$2\left(3xy+2yx^{2}\right)$$
$$xy\left(3+2x\right)$$
$$2xy\left(2x+3\right)$$
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