The current kinetic energy (when 1 m from the plate) is 6×10^8 J. I don't think you have to find the velocity .. just use

Conservation of Energy.

The change of Kinetic Energy is -6×10^8 J when the velocity has fallen to zero.

The change of electric potential is deltaV = E*d (Volts)

so multiply by Q to get the change of potential energy (V*C = J);

Q*E*d = 6×10^8 J

The only unknown is d.

I get d=0.531 m .. same as you .. final position 0.469 m from plate

Have you checked that all the numbers are as given? Why do you believe the correct answer is 0.266 m?