\(\sqrt{8+\sqrt{60}}-\sqrt{\dfrac{2}{\sqrt{15}+4}}=\sqrt{8+2\sqrt{15}}-\dfrac{2}{\sqrt{8+2\sqrt{15}}}=\dfrac{8+2\sqrt{15}-2}{\sqrt{5+2\sqrt{5}.\sqrt{3}+3}}=\dfrac{6+2\sqrt{15}}{\sqrt{5}+\sqrt{3}}=\dfrac{2\sqrt{3}\left(\sqrt{3}+\sqrt{5}\right)}{\sqrt{5}+\sqrt{3}}=2\sqrt{3}\)