Neutra solea puellae bona est; itaque illa ad sutorem postridie redibit.

Because neutra means neither of two, and Latin treats that as singular. The idea is not either sandal taken one at a time, so the noun is singular (solea) and the verb is singular (est).

So:

• neutra solea = neither sandal
• est = is

Latin is not saying the sandals are not good as a pair; it is saying each sandal, considered separately, is not good.

Because bona agrees with solea, not with puellae.

In Latin, an adjective must match its noun in:

• gender
• number
• case

Here:

• solea is feminine
• singular
• nominative

So the adjective must also be feminine nominative singular:

• bona = good

That is why Latin has bona est, not bonum est or bonae sunt.

The form puellae could be either:

• genitive singular = of the girl
• dative singular = to/for the girl

Here it is most naturally understood as genitive singular: of the girl.

So:

• neutra solea puellae = neither sandal of the girl
  or more natural English:
• neither of the girl's sandals

Context helps you decide. Since puellae is closely connected with solea, it is most naturally a possessive genitive here.

Because neutra means neither of two, while nulla means no or not any.

That distinction matters here:

• neutra solea = neither sandal
• nulla solea = no sandal

Since the sentence is talking about a pair of sandals and says that not one or the other is good, neutra is the right word.

Itaque means and so, therefore, or accordingly.

It shows that the second clause follows logically from the first:

• Neither sandal is good
• therefore she will go back to the shoemaker

So itaque is stronger than a simple and. It marks a result or conclusion.

Grammatically, illa is the feminine singular form of ille, illa, illud, meaning that.

But in context, Latin often uses demonstratives like this as pronouns referring back to someone already mentioned. So here illa can be translated naturally as:

• she
• or more literally, that girl

Latin could even have left the subject unstated, because redibit already tells you she/he/it will return. Using illa makes the reference clearer or slightly more emphatic.

Because ad takes the accusative case when it means to or toward.

The noun is:

• sutor = shoemaker, cobbler

Its accusative singular is:

• sutorem

So:

• ad sutorem = to the shoemaker

This is a very common Latin pattern:

• ad
  • accusative for motion toward a person or place.

Postridie is an adverb, and it means the next day or on the following day.

It does not change its form here; it is not agreeing with anything. It simply tells when she will return:

• postridie redibit = she will return the next day

Redibit is the future tense, third person singular, of redeo, redire, meaning return or go back.

So:

• redibit = he/she/it will return

Since the subject is illa, the meaning is:

• she will return

This verb is a compound related to eo (go), and that is why its future has the -ibit pattern.

It may look unusual from an English point of view, but it is normal Latin.

Latin word order is more flexible because the endings show the grammatical relationships. English depends much more on position.

Here Latin places:

• neutra solea first, giving prominence to neither sandal
• bona est at the end, which is a very natural place for the predicate

So the sentence is not odd Latin; it is just less rigidly arranged than English would be.