$$(4\sqrt{3}-2\sqrt{2})(\sqrt{2}+\sqrt{3})$$
$2\left(\sqrt{6}+4\right)\approx 12.898979486$
$$4\sqrt{3}\sqrt{2}+4\left(\sqrt{3}\right)^{2}-2\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}$$
$$4\sqrt{6}+4\left(\sqrt{3}\right)^{2}-2\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}$$
$$4\sqrt{6}+4\times 3-2\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}$$
$$4\sqrt{6}+12-2\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}$$
$$4\sqrt{6}+12-2\times 2-2\sqrt{2}\sqrt{3}$$
$$4\sqrt{6}+12-4-2\sqrt{2}\sqrt{3}$$
$$4\sqrt{6}+8-2\sqrt{2}\sqrt{3}$$
$$4\sqrt{6}+8-2\sqrt{6}$$
$$2\sqrt{6}+8$$
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$2 {(\sqrt{6} + 4)} = 12.898979486$
