In order to calculate R_th, you have to made all voltage and current sources equal to 0 (creating open circuits at current sources and shorts at voltage sources), so you will wind up with only resistors. That means that:
$$R_{th}=[(R_1+R_2)^{-1}+1/R_3+1/R_4]^{-1}$$
The dependent voltage source has a transresistance, so it adds on to the value of R_th. This is not being accepted as my answer though. I tried with and without the transresistance, even though it shouldn't be removed.