$\Delta \gt 0\Rightarrow {{(2m-4)}^{2}}-4(m-2)(m-4) \gt 0$  $4{{m}^{2}}-16m+16-4({{m}^{2}}-6m+8) \gt 0$  $4{{m}^{2}}-16m+16-4{{m}^{2}}+24m-32\gt 0$  $\left\{ \begin{matrix}8m-16\gt 0\Rightarrow m\gt 2  \\ \frac{c}{a}\lt 0\Rightarrow \frac{m-4}{m-2}\lt 0\Rightarrow 2\lt m\lt 4  \\ \end{matrix} \right.\xrightarrow{\bigcap }2\lt m\lt 4$