To find the Thevenin equivalent resistance across the terminals of a 6 Ω resistor after it has been removed from a circuit with a 12 V battery in series with two resistors (4 Ω and 6 Ω), follow these steps:

1. Understand the Problem:
   • We are given a series circuit with a 12 V battery and two resistors (4 Ω and 6 Ω).
   • We need to determine the Thevenin equivalent resistance across the terminals of the 6 Ω resistor, which involves the remaining part of the circuit after we "remove" the 6 Ω resistor.
2. Identify the Circuit after Removing the 6 Ω Resistor:
   • Removing the 6 Ω resistor leaves only the 4 Ω resistor connected to the battery.
3. Thevenin Resistance Calculation:
   • To find the Thevenin equivalent resistance, all independent voltage sources need to be replaced by a short circuit, and all independent current sources by an open circuit.
   • In this case, we replace the 12 V battery with a wire (short circuit).
   • The remaining circuit consists of only the 4 Ω resistor.
   • Thevenin equivalent resistance is just the resistance of the resistor left, which is 4 Ω.
4. Result and Conclusion:
   • After performing the required steps, we find that the Thevenin equivalent resistance across the terminals of the 6 Ω resistor is 4 Ω.

Thus, the correct answer is 4 Ω.