Answer
The $\Delta$$E_{mec}$ due to $F_{nc}$ is -2J.
Work Step by Step
The second path from the top has a $\Delta$$E_{mec}$ of 10J. All the other paths have a $\Delta$$E_{mec}$ of 12J. For this reason, that second path must be the one with non-conservative forces. These forces account for the loss of 2J.
