Two point charges A and B of magnitude   $+8\times {10}^{-6}C$and  $-8\times {10}^{-6}C$ respectively are placed at a distance d apart. The electric field at the middle point O between the charges is $6.4\times {10}^{4}N{C}^{-1}$ . The distance ‘d’ between the point charges A and B is

The magnitude of electric field due to chanrge at point A is
$E_A=\left|\overrightarrow{E}\right|=\frac{1}{4\pi {\epsilon }_0}\frac{8\times {10}^{-6}}{{\left(d/2\right)}^2}=\frac{1}{4\pi {\epsilon }_0}\frac{32\times {10}^{-6}}{d^2}$
The magnitude of electric field due to charge at point B is 
$E_B=\left|\overrightarrow{E}\right|=\frac{1}{4\pi {\epsilon }_0}\frac{8\times {10}^{-6}}{{\left(d/2\right)}^2}=\frac{1}{4\pi {\epsilon }_0}\frac{32\times {10}^{-6}}{d^2}$
Resultant electric field at point C due to two charges is
$E_R=2E=\frac{1}{4\pi {\epsilon }_0}\frac{64\times {10}^{-6}}{d^2}$ or $6.4\times {10}^4=\frac{1}{4\pi {\epsilon }_0}\frac{64\times {10}^{-6}}{d^2}$  Or $d^2=\frac{9\times {10}^9\times 64\times {10}^{-6}}{6.4\times {10}^4}=9$ or $d=3m$