Cause \(2\cdot\left(3+4\right)>2\cdot3+4\)

So the positive difference between the value of 2 × (3 + 4) and the value of 2 × 3 + 4 is :

\(2\cdot\left(3+4\right)-\left(2\cdot3+4\right)=14-10=4\)

Answer : 4.