$$(\frac{4}{2}x^{2}yz)\times(\frac{1}{3}y^{2}zx)\times(-6xyz^{2})$$
$-4\left(xyz\right)^{4}$
$$\frac{4}{2}x^{3}yz\times \frac{1}{3}y^{2}z\left(-6\right)xyz^{2}$$
$$\frac{4}{2}x^{4}yz\times \frac{1}{3}y^{2}z\left(-6\right)yz^{2}$$
$$\frac{4}{2}x^{4}y^{3}z\times \frac{1}{3}z\left(-6\right)yz^{2}$$
$$\frac{4}{2}x^{4}y^{4}z\times \frac{1}{3}z\left(-6\right)z^{2}$$
$$\frac{4}{2}x^{4}y^{4}z^{2}\times \frac{1}{3}\left(-6\right)z^{2}$$
$$\frac{4}{2}x^{4}y^{4}z^{4}\times \frac{1}{3}\left(-6\right)$$
$$2x^{4}y^{4}z^{4}\times \frac{1}{3}\left(-6\right)$$
$$\frac{2}{3}x^{4}y^{4}z^{4}\left(-6\right)$$
$$-4x^{4}y^{4}z^{4}$$
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$-16x^{3}\left(yz\right)^{4}$