Uxor et maritus pactum breve signant, ut argentarius sciat quando debitum solvendum sit.

Latin has no articles. There is no separate word for the or a/an.

So:

• uxor can mean wife or the wife
• maritus can mean husband or the husband

You decide from context which English translation sounds natural.

Because the subject is plural: uxor et maritus = the wife and the husband.

A plural subject takes a plural verb:

• signat = he/she signs
• signant = they sign

So uxor et maritus signant means the wife and husband sign.

• uxor: nominative singular

• maritus: nominative singular
  These are the subjects of signant.

• pactum: accusative singular neuter
  This is the direct object: the thing being signed.

• breve: accusative singular neuter
  This agrees with pactum and means short/brief.

So pactum breve = a short agreement or the short agreement.

Because the adjective has to agree with the noun in gender, number, and case.

Pactum is:

• neuter
• singular
• accusative

So the adjective must also be neuter singular accusative:

• breve

The dictionary form of the adjective is brevis, breve, but here the correct form is breve to match pactum.

Pactum literally means agreement, compact, or bargain.

In this sentence it refers to some kind of agreement the wife and husband sign. Depending on context, English might translate it as:

• agreement
• contract
• arrangement

But grammatically it is just the direct object of signant.

Here ut introduces a purpose clause.

So:

• signant = they sign
• ut argentarius sciat = so that the banker may know

The idea is:

They sign a short agreement so that the banker knows / may know ...

A purpose clause answers for what purpose? or why?

Because after ut in a purpose clause, Latin normally uses the subjunctive.

So:

• scit = he knows (indicative)
• sciat = he may know / would know (subjunctive in a purpose clause)

In this sentence, sciat does not mean the banker already knows as a simple fact. It expresses the purpose of signing:

They sign ... so that the banker may know ...

Because argentarius is the subject of sciat.

In the clause:

ut argentarius sciat

the banker is the one doing the knowing. Therefore he is in the nominative case.

So:

• argentarius = the banker
• subject of sciat

Here quando introduces an indirect question:

when the debt is to be paid / when the debt must be paid

It depends on sciat:

• argentarius sciat = the banker may know
• know what?
• quando debitum solvendum sit = when the debt must be paid

So this is not a relative clause and not a simple statement. It is an embedded question: when?

Because quando debitum solvendum sit is an indirect question, and indirect questions in Latin normally take the subjunctive.

So:

• est = indicative
• sit = subjunctive

The structure is:

• sciat = may know
• quando ... sit = when ... may be / when ... is supposed to be

So both sciat and sit are subjunctive, but for different reasons:

• sciat because of the purpose clause after ut
• sit because of the indirect question after quando

Here debitum means the debt or what is owed.

It is neuter singular nominative in this clause because it is the subject of solvendum sit.

That may feel strange to an English speaker, because in English we focus on the action pay the debt, but in Latin the expression is built as:

the debt is to be paid

So debitum is the thing that is to be paid.

This is a passive periphrastic: a form made from a gerundive plus sum.

• solvendum = gerundive of solvere (to pay)
• sit = subjunctive of esse (to be)

Together they mean something like:

• is to be paid
• must be paid
• should be paid

So:

debitum solvendum sit = the debt must be paid / the debt is to be paid

Because the clause is an indirect question, sum appears in the subjunctive form sit.

Because it agrees with debitum.

In a passive periphrastic, the gerundive acts like an adjective and must match the noun it goes with.

Since debitum is:

• neuter
• singular
• nominative

the gerundive must also be:

• neuter
• singular
• nominative

So we get solvendum.

Yes, there is an idea of obligation. The passive periphrastic often carries the sense:

• must be paid
• has to be paid
• is to be paid

So the phrase does not just describe a future event. It suggests something scheduled, required, or owed.

That is why when the debt must be paid is often a better explanation than a plain when the debt will be paid.

Latin word order is much freer than English word order because the endings show the grammatical relationships.

English relies heavily on position:

• The husband signs the agreement

Latin can move words around more easily because the endings already tell you who is doing what.

In this sentence:

• uxor et maritus are clearly the subjects
• pactum breve is clearly the object
• ut argentarius sciat is clearly a purpose clause
• quando debitum solvendum sit is clearly an indirect question

So the order is natural Latin, even though English would usually keep a more fixed order.

Yes. English can render this in several ways depending on context:

• when the debt must be paid
• when the debt should be paid
• when the debt is to be paid
• when payment of the debt is due

The Latin grammar points to obligation or scheduled necessity, but the exact English wording can vary. The most literal-feeling translation is often when the debt is to be paid, while the most natural English may be when the debt must be paid or when the payment is due.