Answer
Option b.
Work Step by Step
Recall that the Galilean transformation equations are:
$\displaystyle \vec{E}_B = \vec{E}_A + \vec{v} \times \vec{B}_A$
$\displaystyle \vec{B}_B = \vec{B}_A - \frac{1}{c^2}\vec{v} \times \vec{E}_A$
In the diagram shown, the electric field is in the +$\hat k$ direction and the magnetic field is in the +$\hat i$ direction. The direction of the velocity of reference frame B is also in the +$\hat i$ direction. All we have to do is plug the unit vectors into the Galilean transformation equations to find the directions of the vectors in reference frame B.
$\vec{E}_B = \hat k + [(+\hat i) \times (+\hat i)] = \hat k + 0 = \hat k$
$\vec{B}_B = \hat i - [(+\hat i) \times (+\hat k)] = \hat i - (-\hat j) = \hat i + \hat j$
Therefore, the diagram for reference frame B must have an electric field pointing in the positive $z$ direction (+$\hat k$) and have a magnetic field pointing in both the positive $x$ and $y$ directions ($\hat i + \hat j$). The only diagram that has this is option b.
Option b. is correct.
