$$(3 \sqrt{ 2 } - \sqrt{ 3 } )(4 \sqrt{ 3 } - \sqrt{ 2 }$$
$13\sqrt{6}-18\approx 13.843366656$
$$12\sqrt{3}\sqrt{2}-3\left(\sqrt{2}\right)^{2}-4\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-3\left(\sqrt{2}\right)^{2}-4\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-3\times 2-4\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-6-4\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-6-4\times 3+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-6-12+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-18+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-18+\sqrt{6}$$
$$13\sqrt{6}-18$$
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$13 \sqrt{6} - 18 = 13.843366656$
