\textbf{127.} In a regular quadrilateral pyramid, every face is an equilateral triangle. The length of each lateral edge is $2\sqrt{6}$ units. What is the height of this pyramid?
\hspace{1cm} (1) $2\sqrt{7}$ \hspace{2cm} (2) $2\sqrt{r}$ \hspace{2cm} (3) $r$ \hspace{2cm} (4) $f$