To determine the Thevenin's equivalent resistance across terminals A and B, we need to follow these steps:

1. Remove any independent sources present in the circuit. This involves shorting voltage sources and opening current sources. In this circuit, short the 40V and 60V sources.
2. Redraw the circuit with the isolated terminals A and B:

1. Calculate the equivalent resistance between terminals A and B:
   • The 2Ω resistors are in parallel in their respective branches. The equivalent resistance for each parallel combination is calculated using the formula:
   • \(R_{\text{eq, parallel}} = \frac{1}{\frac{1}{2} + \frac{1}{2}} = 1 \text{ Ω}\)
   • Each set of parallel resistors (both left and right clusters) reduces to 1Ω, so you now have two 1Ω resistors in series when terminals A and B are considered open:
   • \(R_{\text{series}} = 1 + 1 = 2 \text{ Ω}\)
   • The two series 2Ω resistances are in parallel with the open terminals:
   • The overall Thevenin resistance is given by:
   • \(R_{\text{th}} = \frac{1}{\frac{1}{2} + \frac{1}{2}} = 0.33 \text{ Ω}\)
2. Hence, the Thevenin's equivalent resistance across terminals A and B is \(0.33 \text{ Ω}\).

Therefore, the correct answer is \(0.33 \text{ Ω}\).