Answer
$-63J$ for all 3 paths
Work Step by Step
We can find the required work done along the given three paths as follows:
Work done for path 1:
$W_1=mg(-y_1+0+y_2+0+y_3)$
We plug in the known values to obtain:
$W_1=(3.2)(9.81)(-4.0+1.0+1.0)=-63J$
Work done for path 2:
$W_2=mg(0-y_4+0)$
We plug in the known values to obtain:
$W_2=(3.2)(9.81)(-2.0)=-63J$
Work done for path 3:
$W_3=mg(y_5+0-y_6)$
We plug in the known values to obtain:
$W_2=(3.2)(9.81)(1.0-3.0)=-63J$
