A force rising steadily from zero to 120 N stretches a wire by 1.6 mm…

Step 1. First stage. $\tfrac12 \times 120\ \text{N} \times 1.6 \times 10^{-3}\ \text{m} = 0.096\ \text{J}$.

Step 2. Total. $\tfrac12 \times 240\ \text{N} \times 3.2 \times 10^{-3}\ \text{m} = 0.384\ \text{J}$.

Step 3. Extra. $0.384\ \text{J} - 0.096\ \text{J} = 0.288\ \text{J}$.