Step 1: The idea being tested.
We need to know what an inhibitory neurotransmitter does to the next (post-synaptic) nerve cell.
Step 2: Resting state of a neuron.
At rest the inside of a neuron is slightly negative compared to the outside. To fire an action potential the inside must become more positive (reach threshold).
Step 3: What inhibition means.
An inhibitory neurotransmitter does the opposite of exciting. It makes the inside of the cell even more negative than before. This moving further from threshold is called hyperpolarization.
Step 4: Why the other options are wrong.
Depolarization makes the cell more positive and helps it fire, that is excitation. An action potential is the firing itself. Repolarization is the recovery phase after firing. None of these is the job of an inhibitory signal.
Step 5: Result.
By making the membrane more negative, the inhibitory neurotransmitter lowers the chance of firing.
Step 6: Conclusion.
Therefore the correct answer is "Hyperpolarization". \[ \boxed{\text{Hyperpolarization}} \]