Answer
The speed increases by a factor of 2.
Work Step by Step
The potential energy gained or lost by the electron is proportional to the accelerating voltage.
Here, the voltage is multiplied by 4, so the initial potential energy is also multiplied by a factor of 4. This potential energy is converted to kinetic energy, so the final kinetic energy has increased by a factor of 4.
KE scales as the speed squared, $KE = \frac{1}{2}mv^{2}$, so the speed increases by a factor of 2.
