1. Potential energy of a dipole in a uniform electric field

   The potential energy is $U = -pE\cos\theta$ where:

   • $p = 6 \times 10^{-6}\ \text{C m}$
   • $E = 10^6\ \text{V/m}$
   • $\theta$ is the angle between dipole moment and electric field.

2. Initial position

   Initially, the dipole is parallel to the field, so $\theta_i = 0^\circ$ Hence, $U_i = -pE\cos 0^\circ = -pE$

3. Final position

   Finally, the dipole is opposite to the field, so $\theta_f = 180^\circ$ Hence, $U_f = -pE\cos 180^\circ = +pE$

4. Work done by external agent

   The work required to rotate the dipole slowly against the field is equal to the increase in potential energy: $W = U_f - U_i = pE - (-pE) = 2pE$

5. Substitute values

   $W = 2 \times (6 \times 10^{-6}) \times (10^6)$

   $W = 2 \times 6 = 12\ \text{J}$

6. Final answer

   $\boxed{12}$

The derived answer matches the stored correct answer.