Answer
65 cm.
Work Step by Step
The net field is zero at point P. Set the magnitudes of the fields created by Q1 and by Q2 to be equal. Let x be a positive number representing the desired distance.
$$k\frac{|Q1|}{x^2}= k\frac{|Q2|}{(x+0.12m)^2}$$
$$k\frac{32\times10^{-6}C}{x^2}= k\frac{45\times10^{-6}C }{(x+0.12m)^2}$$
The constant k cancels out. Solve for x.
$$x=(0.12m)\frac{\sqrt{32\times10^{-6}C}}{\sqrt{45\times10^{-6}C}-\sqrt{32\times10^{-6}C}}$$
$$x=64.57\times10^{-2}m\approx 65\;cm$$