(i) For determining V_{\text {Th }} :

Here, V _{ Th }= V _x , so

\begin{aligned} & -\frac{V_{ Th }}{4000}+\frac{V_{ Th }}{2000}=0 \\ & -V_{ Th }+2 V_{ Th }-8=0 \\ & V_{ Th }=8 \text { Volts } \end{aligned}

(ii) For determining R_{ Th } :
Consider the following equivalent circuits

\begin{aligned} & I_{ sc }=\frac{4}{5000}=0.8  mA \\ & R_{ Th }=\frac{V_{ Th }}{I_{ sc }}=\frac{8}{0.8}=10  k \Omega \end{aligned}