Answer
We can rank the pairs according to the current density:
$(top-bottom) ~\gt~ (front-back) ~\gt ~(left-right)$
Work Step by Step
Note that $\rho$ is the resistivity of the material.
We can find an expression for the current density in each case:
left-right:
$J = \frac{E}{\rho} = \frac{V}{\rho~d} = \frac{V}{\rho~(3L)} = \frac{1}{3}\cdot \frac{V}{\rho~L}$
top-bottom:
$J = \frac{E}{\rho} = \frac{V}{\rho~L}$
front-back:
$J = \frac{E}{\rho} = \frac{V}{\rho~d} = \frac{V}{\rho~(2L)} = \frac{1}{2}\cdot \frac{V}{\rho~L}$
We can rank the pairs according to the current density:
$(top-bottom) ~\gt~ (front-back) ~\gt ~(left-right)$
