Answer
We can rank the pairs according to the current:
$(top-bottom) ~\gt~ (front-back) ~\gt ~(left-right)$
Work Step by Step
Note that $\rho$ is the resistivity of the material.
We can find an expression for the current in each case:
left-right:
$i = \frac{V}{R}$
$i = \frac{V}{(\rho~d)/A}$
$i = \frac{V~A}{\rho~d}$
$i = \frac{V~(L)(2L)}{\rho~(3L)}$
$i = \frac{2}{3}\cdot \frac{V~L}{\rho}$
top-bottom:
$i = \frac{V}{R}$
$i = \frac{V}{(\rho~d)/A}$
$i = \frac{V~A}{\rho~d}$
$i = \frac{V~(3L)(2L)}{\rho~(L)}$
$i = 6\cdot \frac{V~L}{\rho}$
front-back:
$i = \frac{V}{R}$
$i = \frac{V}{(\rho~d)/A}$
$i = \frac{V~A}{\rho~d}$
$i = \frac{V~(L)(3L)}{\rho~(2L)}$
$i = \frac{3}{2}\cdot \frac{V~L}{\rho}$
We can rank the pairs according to the current:
$(top-bottom) ~\gt~ (front-back) ~\gt ~(left-right)$
