Answer
The force does work at a rate of $~~28.0~W$
Work Step by Step
We can find the i-component of the rate of work:
$P_i = F_i~v_i$
$P_i = (4.0~N)(-2.0~m/s)$
$P_i = -8.0~W$
We can find the j-component of the rate of work:
$P_j = F_j~v_j$
$P_j = (-2.0~N)(0~m/s)$
$P_j = 0$
We can find the k-component of the rate of work:
$P_k = F_k~v_k$
$P_k = (9.0~N)(4.0~m/s)$
$P_k = 36.0~W$
We can find the rate at which the force does work:
$P = -8.0~W+36.0~W = 28.0~W$
The force does work at a rate of $~~28.0~W$
