How does hyperpolarization affect the threshold potential?

Hint: Hyperpolarisation takes place in the membrane of the neurons. It happens when the membrane potential becomes more negative. It inhibits the action potential by elevating the stimulus required so as the change membrane potential to action potential threshold. It is the reverse of depolarisation.

Complete answer:
To solve this question, we must know about the mechanism of attaining threshold potential.
The threshold potential is the level to which the depolarisation must take place in the membrane potential so that an action potential can be attained. The threshold potential is important to control and distribute the signals in both the central and peripheral nervous system. The threshold valve controls the incoming stimuli and sees whether it is able to generate action potential or not.
 The threshold potential is in between -50 and -55mV. The resting potential of neurons is -70mV. This can increase or decrease through sodium and potassium ions. The entry of the sodium inside the cell through a voltage-gated sodium channel can lead to depolarisation of the membrane beyond threshold. This will trigger the membrane potential. But the efflux of potassium or chloride can lead to hyperpolarization of the cell. Hyperpolarization is the last step in action potential. As a result of which threshold potential cannot be attained.

Note:
The change in the threshold valve either increase or decrease is due to the change in the sodium or potassium ions. The diameter of the axons and the voltage of the sodium channels in the axons have an effect on the threshold value. The hyperpolarisation helps in preventing the stimulus which is already sent to an axon from initiating the action potential in the opposite direction.