Learn Hardcore Latin: Inopia panis matrem tristem facit. - The lack of bread makes the mother sad.

Because inopia is in the nominative singular, the case normally used for the subject. The verb facit is also 3rd person singular, so it matches inopia: shortage/lack ... makes.

Why is panis not panem?

Here panis is genitive singular, not accusative. With nouns like inopia (lack, shortage), Latin often uses the genitive to show what is lacking.

So:

inopia panis = lack of bread / shortage of bread

This is a very common Latin pattern: a noun of lacking, need, fullness, memory, and so on can take a genitive dependent on it.

How can I tell that panis is genitive singular?

Because panis is a 3rd-declension noun, and in this noun the nominative singular and genitive singular happen to look the same:

nominative: panis
genitive: panis

So you have to decide from the grammar of the sentence. Since inopia naturally takes a genitive, panis here is understood as genitive singular: of bread.