The electrons that produce the picture in a

TV set are accelerated by a very large electric
force as they pass through a small region in
the neck of the picture tube. This region is
1.9 cm in length, and the electrons enter with
a speed of 1 × 10^5 m/s and leave with a speed
of 2.5 × 10^6 m/s.

a = 1.642105263E14 m/s^2

Need the time in s, please help

v = v0 + at

so, plug in your numbers
10^5 + 1.642105263*10^14 t = 2.5*10^6
t = 1.46154*10^-8 s
the length of the neck does not matter, since they gave you both starting and ending speeds, and the acceleration. I guess you could check to make sure that your value for t fits the distance function
s = v0t + 1/2 at^2