Pater et mater de disciplina inter se conveniunt.

They are both in the nominative singular, which is the case normally used for the subject of the sentence.

• pater = father
• mater = mother

Since these are the two people doing the action, Latin puts them in the nominative.

Because the subject is two people: pater et mater.

So even though each noun is singular by itself, together they make a plural subject, and the verb must match:

• convenit = he/she/it agrees or comes together
• conveniunt = they agree or come together

Here conveniunt means they agree.

The verb convenio, convenire can have a few related meanings, such as:

• come together
• meet
• agree

In this sentence, because of de disciplina and inter se, the meaning is clearly they agree with each other about discipline/education.

Disciplina is in the ablative singular because it follows the preposition de.

The preposition de commonly means:

• about
• concerning
• regarding

So:

• de disciplina = about discipline / about education / about training

Inter se means with each other, among themselves, or between themselves.

It is a very common Latin expression:

• inter = among, between
• se = themselves, each other (reflexive pronoun)

So inter se conveniunt means they are in agreement with one another.

Latin often expresses this idea with inter se rather than with a single separate word exactly like English each other.

English says:

• They agree with each other

Latin often says:

• They agree among themselves / between themselves

That is why inter se is a very natural Latin way to show mutual action.

Because Latin has no articles.

Latin does not have separate words for:

• the
• a
• an

So pater can mean:

• father
• the father
• a father

And mater can mean:

• mother
• the mother
• a mother

You understand which one is meant from the context.

Because inter se already gives the idea of mutual relationship: with each other / among themselves.

Latin can use different constructions depending on the verb and the nuance. Here:

• de disciplina tells us what they agree about
• inter se tells us that the agreement is between them

So there is no need for cum in this sentence.

Sometimes, but not always exactly.

Latin disciplina can mean things like:

• instruction
• teaching
• training
• education
• discipline

So depending on context, de disciplina might mean:

• about education
• about training
• about discipline

A learner should not assume it always means only the modern English sense of discipline.

Latin word order is much freer than English word order because Latin shows grammatical relationships mostly through endings, not position.

English usually depends heavily on order:

• The father and mother agree with each other about discipline

Latin can move parts around more easily:

• Pater et mater de disciplina inter se conveniunt
• Pater et mater inter se de disciplina conveniunt

Both are understandable. The chosen order may reflect emphasis or style, not a basic change in meaning.

You know from the case endings and from the verb.

• pater and mater are nominative forms
• conveniunt is a finite verb meaning they agree

Since Latin marks subjects by case, a reader sees that pater et mater are the ones doing the agreeing.

Also, this sentence does not contain a direct object. Instead, it has:

• a subject: pater et mater
• a prepositional phrase: de disciplina
• a mutual expression: inter se
• a verb: conveniunt

By itself, conveniunt can sometimes mean they come together or they meet. But in this sentence, de disciplina strongly points toward the sense they agree about something.

So although the verb has multiple possible meanings in Latin, here the most natural meaning is:

• The father and mother agree with each other about discipline/education.