Hard to tell what you don't understand.
I may be wrong in what I'm laying out here, but I go by concept rather than slavishly thinking the printed word is always accurate, even in textbooks.
In lay terms:
Remember when you scuffed your feet on a carpet and generated a static electricity charge that zapped you when you touched a doorknob. Now imagine you are holding another doorknob as you approach the doorknb that zapped you. When you get really close with that doorknob extended in front of you, but not close enough to create the spark, that is a crude representation of the synapse.
Now, since the electricity in an example synapse is "created" by calcium ++ ions, the doorknob in your hand will be called the axon, and when activated the ++ charge will want to neutralize (go to zero electric potential) by crossing the space between doorknobs (synaptic cleft) to receptors located on the other doorknob (dendrite)
So, if you WANT to create a spark (have an agonist), you want the doorknob in your hand to be even more positive, or make the pathway between doorknobs MORE conductive. If you don't want a spark to fire (antagonist) you want to make the axon more negative (reduce the ++ charge buildup) or insulate the two doorknobs more effectively.
In what you presented, this appears to be incorrect:
An inhibitory neurotransmitter makes the postsynaptic neuron _________ likely to fire an action potential by making the inside of the
postsynaptic neuron more ___________.
It should read:
An inhibitory neurotransmitter makes the neuron _________ likely to fire an action potential by making the inside of the neuron more ___________.
Postsynaptic refers to the dendrite, not the axon.
The book may be trying to make a simple example, but it relates more specifically to calcium channel blockers and GABA than the complex actions that occur in other areas.
Hmmm... here - this should get you on the right track:
https://en.wikipedia.org/wiki/Neurotransmitter