Hello!
I'm unfamiliar with the book you are reading,
However, based on textual evidence, I think your answer relies somewhere in answer choice A or D.
I hope this helps!
Momentum
mava + mbvb = mava '+ mbvb'
(300 x 10)+(150 x 0) = (300 x 4.12)+(150 x vb')
3000=1236+150vb'
1764 = 150vb'
vb'=+11.76 m/s ≈ +11.8 m/s (positive sign, to the right)
1) In the reference frame of one electron: 0.38c
To find the relative velocity of one electron with respect to the other, we must use the following formula:

where
u is the velocity of one electron
v is the velocity of the second electron
c is the speed of light
In this problem:
u = 0.2c
v = -0.2c (since the second electron is moving towards the first one, so in the opposite direction)
Substituting, we find:

2) In the reference frame of the laboratory: -0.2c and +0.2c
In this case, there is no calculation to be done. In fact, we are already given the speed of the two electrons; we are also told that they travel in opposite direction, so their velocities are
+0.2c
-0.2c