The equivalent resistance of a circuit refers to the total resistance that would replace all the individual resistances in the circuit while maintaining the same current flow. In this particular circuit, we need to calculate the equivalent resistance.

Option 1: 12Ω

This is not the correct answer, as it does not accurately represent the equivalent resistance of the circuit.

Option 2: 8Ω

This is not the correct answer either, as it also does not accurately represent the equivalent resistance of the circuit.

Option 3: 9Ω

This is the correct answer. To understand why, we need to analyze the circuit. The circuit consists of three resistors in parallel: a 4Ω resistor, a 6Ω resistor, and a 12Ω resistor. When resistors are in parallel, the total resistance is calculated using the formula: 1/Req = 1/R1 + 1/R2 + 1/R3. In this case, 1/Req = 1/4 + 1/6 + 1/12. Simplifying this equation gives us 1/Req = 3/6 + 2/6 + 1/6, which is equal to 6/6, or