urgent help for this networks sac

[kk243]

question 6 vcaa 2008 exam 1 networks module

wHAT I did to solve this question is 6 + 6 + 8  + 9 + 7 + 4 + 4 = 44
however the answer is 42 which is obtained through 6 + 6 + 8 + 9 + 7 + 2 + 4 = 42

how come the 4 is omitted and the 2 which goes backwards is included in the calculation of the capacity of the cut.

thanks in advanced

[plato]

Try shading everything on the left hand side of the cut. The shaded side is the source side and the unshaded side is the sink side.

You ignore any edge that goes from the unshaded part (sink) to the shaded part (source). The 4 must be ignored but the 2 goes from the shaded side (source) to the unshaded side and so must be counted.