Answer
$\tau = (12~N\cdot m)~\hat{j}$
Work Step by Step
We can write the general form of a cross-product:
$a\times b = (a_yb_z-b_ya_z)~\hat{i}+(a_zb_x-b_za_x)~\hat{j}+(a_xb_y-b_xa_y)~\hat{k}$
We can express the plum's position in unit-vector notation:
$r = (-2.0~m)~\hat{i}+ (4.0~m)~\hat{k}$
We can write the net force in unit-vector notation:
$F =(6.0~N)~\hat{k}$
We can find the torque about the origin on the plum:
$\tau = r \times F$
$\tau = (0)~\hat{i}+[0-(6.0~N)(-2.0~m)]~\hat{j}+(0)~\hat{k}$
$\tau = (12~N\cdot m)~\hat{j}$
