Which branches should I convert for this star-delta transformation?
Homework, only guidance: 

Start by removing the 2 Ohm from AB. Later you will put it back when you have calculated the rest of the circuit. Let Rab be =X when that 2 Ohm is removed. The wanted Rab=X in parallel with 2 Ohm. 

You must do two resistor removals and putting it back to get the result and I showed the first one. Series and parallel resistance formulas are as essential as delta-star formula.

After taking off that 2 Ohm there's only one delta. Convert it to star. Then you hopefully see another possibility to advance towards series-parallel circuit.