Magister dicit discipulos pacem in schola servare debere.

Because this sentence uses indirect statement after dicit (says).

In Latin, after verbs of saying, thinking, knowing, hearing, and similar verbs, the subject of the reported statement usually goes into the accusative, and the verb of that reported statement goes into the infinitive.

So:

• magister dicit = the teacher says
• discipulos ... debere = that the students ought ...

Even though discipulos is the logical subject of debere and servare, Latin puts it in the accusative because it is the subject of an indirect statement.

If this were a direct statement, you would expect:

• discipuli pacem in schola servare debent = the students ought to keep peace in school

But after dicit, that becomes:

• magister dicit discipulos pacem in schola servare debere

This is the accusative-and-infinitive construction, often called indirect statement.

Latin often expresses that-clauses in this way instead of using a word like that.

So English:

• The teacher says that the students ought to keep peace in school

Latin:

• Magister dicit discipulos pacem in schola servare debere.

The pattern is:

• main verb: dicit
• accusative subject of reported statement: discipulos
• infinitive verb of reported statement: debere
• plus anything depending on that infinitive: pacem in schola servare

Because they do two different jobs.

• debere means to owe, and by extension to ought / must / should
• servare means to preserve, keep, maintain

Here, debere is the main verb of the indirect statement:

• discipulos ... debere = that the students ought

Then servare depends on debere:

• servare debere = to ought to keep / to be obliged to keep

So the structure is basically:

• dicit = says
• discipulos debere = that the students ought
• pacem servare = to keep peace
• in schola = in school

In smoother English: The teacher says that the students ought to keep peace in school.

Because pacem is the direct object of servare.

• servare = to keep / preserve / maintain
• What do the students keep? peace
• Therefore peace is the object, and Latin puts it in the accusative:
  • pax = peace
  • pacem = peace as a direct object

So:

• discipulos = accusative because it is the subject of the indirect statement
• pacem = accusative because it is the object of servare

They are both accusative, but for different reasons.

You know this from the construction and from meaning.

In an indirect statement:

• the accusative noun referring to the doer is the subject of the infinitive
• the thing being acted on is the object

Here:

• discipulos = the ones who ought to do something
• pacem = the thing they ought to keep

So:

• discipulos ... debere = the students ought
• pacem servare = to keep peace

Latin readers recognize this pattern very quickly, especially after a verb like dicit.

Because in indirect statement, Latin uses an infinitive where English often uses a finite verb in a that-clause.

English says:

• The teacher says that the students ought...

Latin says:

• Magister dicit discipulos ... debere

If it were not indirect statement, you would have:

• discipuli pacem in schola servare debent

But after dicit, debent changes to debere.

Because Latin usually does not need one in this construction.

English commonly says:

• The teacher says that the students ought to keep peace.

Latin often expresses the same idea simply by using:

• an accusative subject
• an infinitive verb

So instead of a separate word for that, Latin shows the relationship through grammar:

• dicit
  • discipulos ... debere

That whole part means what English would express with that the students ought ...

Because in with the ablative usually means in or on in the sense of location.

• in schola = in school / in the school

If in takes the accusative, it usually suggests movement into something:

• in scholam = into the school

But here there is no movement. It tells you where the peace is to be kept, so Latin uses the ablative:

• in schola

It can often be understood either way depending on context.

Literally, it is in the school. But in natural English, especially in a school context, it may be translated more smoothly as:

• in school
• at school
• in the classroom/school environment

Latin often leaves some of that nuance to context.

Because magister is the subject of the main verb dicit.

• magister = the teacher
• dicit = says

So:

• The teacher says ...

This is separate from the indirect statement inside the sentence. The outer sentence has its own subject and verb:

• magister dicit

Then the reported content follows:

• discipulos pacem in schola servare debere

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

A more mechanically arranged version might be:

• Magister dicit discipulos debere pacem in schola servare.

But the given order:

• Magister dicit discipulos pacem in schola servare debere.

is perfectly normal Latin.

A few helpful points:

• Latin often puts the infinitive of the indirect statement toward the end.
• Words that belong together in meaning do not always stand next to each other.
• Readers track the relationships through endings and syntax, not just position.

So the sentence may look unusual to an English speaker, but it is good idiomatic Latin.

Servare basically means to save, preserve, keep, maintain, or observe, depending on context.

Here pacem servare means:

• to keep the peace
• to maintain peace

This is a very natural phrase in Latin, much like English keep the peace.

Yes, depending on context.

Debere originally means to owe, but very often it expresses duty or obligation. In English, that can be rendered as:

• ought to
• should
• must
• are supposed to

So this sentence could be translated in slightly different ways:

• The teacher says that the students ought to keep peace in school.
• The teacher says that the students should keep peace in school.
• The teacher says that the students must keep peace in school.

The exact force depends on context and tone.

Yes. The direct statement would be:

• Discipuli pacem in schola servare debent.

That means:

• The students ought to keep peace in school.

Then if you add The teacher says that..., Latin changes it into indirect statement:

• Magister dicit discipulos pacem in schola servare debere.

This is a very useful exercise for understanding the construction:

• discipuli → discipulos
• debent → debere

Here is a quick parsing:

• magister
  nominative singular masculine
  teacher

• dicit
  3rd person singular present active indicative of dicere
  says

• discipulos
  accusative plural masculine of discipulus
  students / pupils

• pacem
  accusative singular of pax
  peace

• in schola
  preposition in

  • ablative singular of schola
    in school / in the school

• servare
  present active infinitive of servare
  to keep / preserve

• debere
  present active infinitive of debere
  to ought / to owe / to be obliged

Seeing the forms clearly often makes the sentence much easier to understand.