$$( \sqrt{ 4 } - \sqrt{ 6 } )( \sqrt{ 6 } + \sqrt{ 4 } )/8-3 \sqrt{ 5 }$$
$-3\sqrt{5}-\frac{1}{4}\approx -6.958203932$
$$\frac{\left(\sqrt{4}\right)^{2}-\left(\sqrt{6}\right)^{2}}{8}-3\sqrt{5}$$
$$\frac{4-\left(\sqrt{6}\right)^{2}}{8}-3\sqrt{5}$$
$$\frac{4-6}{8}-3\sqrt{5}$$
$$\frac{-2}{8}-3\sqrt{5}$$
$$-\frac{1}{4}-3\sqrt{5}$$
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$\frac{-12 \sqrt{5} - 1}{4} = -6.958203932499369$
