\(A=\left(\sqrt{14}-\sqrt{2}\right)\sqrt{4+\sqrt{7}}\)
\(=\sqrt{2}\sqrt{4+\sqrt{7}}\left(\sqrt{7}-1\right)\)
\(=\sqrt{8+2\sqrt{7}}\left(\sqrt{7}-1\right)\)
\(=\sqrt{\left(\sqrt{7}+1\right)^2}\left(\sqrt{7}-1\right)\)
\(=\left(\sqrt{7}+1\right)\left(\sqrt{7}-1\right)\)
\(=7-1=6.\)