Answer
10 million.
Work Step by Step
The droplet is stationary, so the upward electric force balances the weight.
Find the mass of the droplet from its volume times the density of water. Let N be the excess number of electron charges on the droplet.
$$|q|E=mg$$
$$NeE=\frac{4\pi}{3}r^3\rho g$$
$$N=\frac{4\pi r^3\rho g }{3eE} $$
$$N=\frac{4\pi (0.000018m)^3(1000kg/m^3) (9.80m/s^2) }{3(1.60\times10^{-19}C)(150N/C)}\approx 1.0\times10^7 $$
