How do you find Thevenin equivalent resistance from this circuit?
That is not how you calculate thevenin equivalent. Not even close. You short the load resistor and measure (calculate) current, and them open the load resistor and calculate voltage and divide the two. And I already solved this identical problem for you or someone else, but again… Short circuit current has two components that add. From left battery, I = 15/470, and the other 10/180, which adds up to 31.9+55.6 = 87.4 mA now with RL open, you have a voltage divider with 5 volts across it, so the voltage is Vt = 10+5(180/(180+470)) = 11.4 volts. So Rth = 11.4 / 87.4 = 130 ohms. Note that R1 has no influence. It is across the battery, so all t does is use up power. .
