\(H=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\\ =\left(\sqrt{4+\sqrt{15}}\right)^2.\sqrt{4-\sqrt{15}}\left(\sqrt{10}-\sqrt{6}\right)\)
\(=\sqrt{\left(4+\sqrt{15}\right)\left(4-\sqrt{15}\right)}.\sqrt{4+\sqrt{15}}\left(\sqrt{10}-\sqrt{6}\right)\\ =1.\sqrt{4+\sqrt{15}}.\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\\ =\sqrt{8+2\sqrt{15}}.\left(\sqrt{5}-\sqrt{3}\right)\\ =\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}\left(\sqrt{5}-\sqrt{3}\right)\\ =\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)\\ =5-3\\ =2\)