Answer
$\vec{B}_c > \vec{B}_a > \vec{B}_d > \vec{B}_b$
Work Step by Step
Ampere's Law is as follows:
$\displaystyle \oint\vec{B}\cdot d\vec{s} = \mu_0(I_{enclosed} + \epsilon_0\frac{d\Phi_E}{dt})$
Since we're given a graph of $\vec{E}$ vs. time, we need to find an equation that relates $\vec{B}$ to $\vec{E}$
$\displaystyle \oint\vec{B}\cdot d\vec{s} = \mu_0(I_{enclosed} + \epsilon_0\frac{d\Phi_E}{dt})$
$\displaystyle \vec{B} = \frac{\mu_0}{\vec{s}}(0 + \epsilon_0\frac{d}{dt}[\oint\vec{E}\cdot d\vec{A}])$
$\displaystyle \vec{B} = \frac{\mu_0\epsilon_0}{2\pi r}(\frac{d\vec{E}}{dt}\vec{A})$
$\displaystyle \vec{B} = \frac{\mu_0\epsilon_0A}{2\pi r} \frac{d\vec{E}}{dt}$
We see that $\vec{B}$ is directly related to $\displaystyle \frac{d\vec{E}}{dt}$. Because the question asks to rank the $strengths$ (which is the same thing as the magnitude) of the magnetic field, then the greater the slope of the line the stronger the magnetic field. Thus, the rankings are:
$\vec{B}_c > \vec{B}_a > \vec{B}_d > \vec{B}_b$
