Soror callida fratri monstrat quomodo menda citius corrigat.

Because callida is an adjective modifying soror, so it has to agree with it in gender, number, and case.

• soror = feminine singular nominative
• callida = feminine singular nominative

So soror callida means a clever sister or the clever sister.

Latin adjectives do not have to stand right next to the noun, but they must agree with it.

Fratri is dative because it is the indirect object of monstrat.

The verb monstrare often works like to show someone something or to show someone how...

So here:

• soror = the sister, the one doing the showing
• fratri = to her brother, the person being shown something

This is very natural Latin:

• alicui monstrare = to show someone

Here monstrat means shows, but in a slightly broader sense than just physically pointing at something. It can also mean:

• demonstrates
• explains
• shows someone how to do something

So in this sentence, the sister is not necessarily pointing at mistakes; she is showing her brother the method or way to correct them.

Quomodo means how.

It introduces a clause explaining the method:

• quomodo menda citius corrigat = how he may correct mistakes more quickly / how to correct mistakes more quickly

This is a very common Latin way to express how something is done.

Because quomodo here introduces an indirect question, and indirect questions in Latin normally take the subjunctive.

So:

• direct question: Quomodo menda corrigit? = How does he correct mistakes?
• indirect question: Soror fratri monstrat quomodo menda corrigat. = The sister shows her brother how he corrects / should correct / can correct mistakes.

The subjunctive is not there because the action is doubtful in a vague English sense; it is there because Latin grammar requires it in this kind of subordinate clause.

The present subjunctive here is used because the action is viewed as happening at the same time as or after the main verb monstrat.

In other words, she is showing him now how he should or can correct mistakes.

So the tense relationship is roughly:

• monstrat = she shows
• corrigat = how he may/should correct

English often uses how to correct instead of showing this tense relationship so clearly.

Most naturally, it is understood to be the brother.

So the sense is:

• The clever sister shows her brother how he can correct mistakes more quickly.

Latin often leaves the subject of a subordinate verb unstated when it can be understood from context.

That said, strictly speaking, corrigat by itself only tells us someone singular is doing the correcting. The context strongly suggests frater, because he is the one being instructed.

Because menda is a neuter plural form.

The singular is:

• mendum = mistake, fault, error

The plural is:

• menda = mistakes

This is normal for second-declension neuter nouns:

• singular nominative/accusative: -um
• plural nominative/accusative: -a

So menda can be either nominative plural or accusative plural. Here it is accusative plural, because it is the direct object of corrigat.

Citius means more quickly.

It is the comparative adverb from cito. In this sentence it modifies corrigat:

• menda citius corrigat = correct mistakes more quickly

Latin often uses a comparative without stating both sides explicitly. So more quickly may mean:

• more quickly than before
• more quickly than usual
• more quickly than someone else

The comparison is understood from context.

Latin often prefers a finite clause with quomodo plus a subjunctive verb:

• quomodo menda citius corrigat

English often compresses this into an infinitive:

• how to correct mistakes more quickly

So the Latin structure is more fully spelled out than the English one. Instead of literally saying how to correct, Latin says something closer to how he may/should correct.

Latin word order is much more flexible than English word order, because the endings show the grammatical roles.

So:

• Soror callida fratri monstrat quomodo menda citius corrigat

could be rearranged in various ways without changing the basic meaning.

Still, the given order is natural:

• Soror callida puts the subject first
• fratri comes before the verb as the indirect object
• the quomodo clause comes after monstrat, where you would expect the explanation of what she is showing

So word order in Latin often affects emphasis and style more than basic grammatical function.

Because Classical Latin has no articles.

So soror callida can mean:

• a clever sister
• the clever sister

And fratri can mean:

• to a brother
• to the brother
• to her brother, if the context makes that clear

English must choose an article, but Latin usually leaves that to context.