$2xzy\sqrt { 12{ x }z }$
$2zy\sqrt { 12{ x }z }$
$2xz\sqrt { 12{ x }z }$
$2xzy\sqrt { 6{ x }z }$

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The original expression is $zy\sqrt {24x^3z}$ . $24 = 2^2 \times 6$ so put the $2$ outside the radical and the 6 inside the radical. $x^3 = x^2 \times x$ so put one x outside the radical and leave one x in the radical. Because there was only one $z$ , nothing could be done to it. So, the simplified expression is $2xzy\sqrt {6xz}$ .