Introduction: In order to find the equivalent resistance between points A and B in the circuit diagram, we need to apply the principles of Ohm's law and Kirchhoff's laws.

Step 1: Simplify the circuit: The first step is to simplify the circuit by combining resistors that are in series or parallel. In this case, we can combine the 4 ohm and 6 ohm resistors that are in parallel to get a total resistance of 2.4 ohms. We can also combine the 3 ohm and 2.4 ohm resistors that are in series to get a total resistance of 5.4 ohms.

Step 2: Apply Kirchhoff's laws: Kirchhoff's laws state that the total current entering a junction is equal to the total current leaving the junction, and that the total voltage around a closed loop in a circuit is equal to zero. We can use these laws to find the current and voltage at different points in the circuit.

Step 3: Calculate the equivalent resistance: Once we have simplified the circuit and found the current and voltage at different points, we can use Ohm's law to calculate the equivalent resistance between points A and B. The equivalent resistance is simply the voltage difference between points A and B divided by the current flowing between them.

Conclusion: In this circuit, the equivalent resistance between points A and B is 5.4 ohms. We can simplify the circuit by combining resistors in series or parallel, and use Kirchhoff's laws to find the current and voltage at different points. Finally, we can use Ohm's law to calculate the equivalent resistance between two points in the circuit.