$\begin{align}  & \frac{AM}{MD}=\frac{BN}{NC}=1\Rightarrow MN\left\| AB \right\|DC \\  & \left. \begin{matrix}   ME\left\| AB \right.\xrightarrow[in\,\,\,\,A\overset{\vartriangle }{\mathop{D}}\,B]{Thales}\frac{ME}{AB}=\frac{DM}{DA}=\frac{1}{2}\Rightarrow ME=\frac{1}{2}AB=4  \\   MF\left\| DC \right.\xrightarrow[in\,\,\,\,D\overset{\vartriangle }{\mathop{A}}\,C]{Thales}\frac{MF}{AD}=\frac{AM}{AD}=\frac{1}{2}\Rightarrow MF=\frac{1}{2}DC=6  \\\end{matrix} \right\}\Rightarrow EF=MF-ME=6-4=2 \\ \end{align}$