Answer
$W = 1.22\times 10^{-23}~J$
Work Step by Step
We can write a general expression for the potential energy:
$U = -p \cdot E = (-p ~E)~cos~\theta$
Initially, the angle between the direction of $p$ and $E$ is $64^{\circ}$
We can write an expression for the initial potential energy:
$U_1 = -pE~cos~64^{\circ}$
After the electric dipole is turned $180^{\circ}$, the angle between the direction of $p$ and $E$ is $116^{\circ}$
We can write an expression for the final potential energy:
$U_2 = -pE~cos~116^{\circ}$
We can find the work required:
$W = \Delta U$
$W = U_2-U_1$
$W = (-pE~cos~116^{\circ})-(-pE~cos~64^{\circ})$
$W = (pE~cos~64^{\circ})-(pE~cos~116^{\circ})$
$W = pE~(cos~64^{\circ} - cos~116^{\circ})$
$W = (3.02\times 10^{-25}~C\cdot m)(46.0~N/C)~(cos~64^{\circ} - cos~116^{\circ})$
$W = 1.22\times 10^{-23}~J$
