use test source to solve thevenin resistor
fireflies, you cannot do that directly in this circuit. You are right,
to find Rth, you have to set the independent sources to zero, but note that this circuit has no independent sources. Do not short circuit the 2I source!
to get Rth, you have to attach at test source at the output terminals a-b. So put a test source of Vtest=10V (with positive at a and negative at b). Then Rth=Vtest/Itest, where Itest is the current coming out of the positive end of Vtest. Why did I choose 10V? Actually, you can choose anything, but with Vtest=10V, the voltage across the 10Ω resistor is 10V so I=1A. With I=1A, the 2I dependent voltage source becomes a voltage source of 2V. Now the voltage across the 5Ω resistor is 8V (- 8V +), with more positive end at the right end of the resistor. So the current flowing in the 5Ω resistor is 8V/5Ω= 8/5 A (this current is flowing from right to left). Now you can calculate Itest (the current that is leaving the + end of Vtest). Itest = current in the 10Ω (from top to bottom) + current in the 5Ω (from right to left). So Itest = 1+8/5 = 13/5A. Now Rth=Vtest/Itest=10V/(13/5)=(50/13)Ω≈3.85Ω
So the thevenin equivalent circuit is just a resistance since Vth=0 (short circuit).
Hope this helps.
Best regards,
v_c