$$(4\sqrt{3}-2\sqrt{2})(3\sqrt{2}+4\sqrt{3})$$
$4\left(\sqrt{6}+9\right)\approx 45.797958971$
$$12\sqrt{3}\sqrt{2}+16\left(\sqrt{3}\right)^{2}-6\left(\sqrt{2}\right)^{2}-8\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}+16\left(\sqrt{3}\right)^{2}-6\left(\sqrt{2}\right)^{2}-8\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}+16\times 3-6\left(\sqrt{2}\right)^{2}-8\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}+48-6\left(\sqrt{2}\right)^{2}-8\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}+48-6\times 2-8\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}+48-12-8\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}+36-8\sqrt{3}\sqrt{2}$$
$$12\sqrt{6}+36-8\sqrt{6}$$
$$4\sqrt{6}+36$$
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$4 {(\sqrt{6} + 9)} = 45.797958971$
