Can potential difference between the terminals of a battery ever be opposite in direction to the emf? If it can, give an example. If it cannot, explain why not.

The potential difference is defined as the work required to move the charge of unit magnitude from a point in the conductor to the other point.

Consider the expression for the voltage at the battery terminals.

$V=\epsilon -iR$

Here, the voltage is the V, the emf of the battery is $\epsilon$, the current is $i$and the resistance is R.

The current moves in the direction from negative to positive when battery have higher emf forces. And when this current reaches to the other potential difference it continuous flow in same direction which is opposite direction to the emf of the battery with lower emf. And the example for this rechargeable battery.

Consider the expression for the voltage at the battery terminals if the current is in the opposite direction.

$V=\epsilon +iR$

Hence,yes potential difference between the terminals of a battery will be opposite in direction to the emf.