Can you suggest any alternative procedure for the determination of thevenin's resistance?

One alternative method to determine Thevenin's resistance is to perform a voltage divider analysis on the circuit. By applying a test voltage source and analyzing the resulting current, you can calculate the Thevenin resistance based on Ohm's Law. Additionally, you could use nodal analysis or mesh analysis techniques to determine Thevenin's resistance by setting up equations based on the circuit components.