The correct option is (a) -(G*M*m)/12R
For explanation I would say: Total energy at 1.5R (TE) = -[(G*M*m)/3R]
Total energy at 2R (TE’) = -[(G*M*m)/4R]
The difference in energy is the required energy.
Difference = TE’ – TE
= -[(G*M*m)/4R] – [-[(G*M*m)/3R]]
= -[(G*M*m)/4R] + (G*M*m)/3R]
= (G*M*m)/12R.