$$(4 \sqrt{ 2 } - \sqrt{ 3 } )(3 \sqrt{ 3 } - \sqrt{ 2 }$$
$13\sqrt{6}-17\approx 14.843366656$
$$12\sqrt{3}\sqrt{2}-4\left(\sqrt{2}\right)^{2}-3\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-4\left(\sqrt{2}\right)^{2}-3\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-4\times 2-3\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-8-3\left(\sqrt{3}\right)^{2}+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-8-3\times 3+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-8-9+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-17+\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}-17+\sqrt{6}$$
$$13\sqrt{6}-17$$
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