Hoc negotium grave est, sed iudex veritatem scit.

Hoc means this.

It is hoc because it agrees with negotium, which is a neuter singular noun. Latin demonstratives must agree with the noun they describe in gender, number, and case.

So:

• hic = this (masculine singular)
• haec = this (feminine singular)
• hoc = this (neuter singular)

Since negotium is neuter singular, Latin uses hoc negotium = this matter / this business / this affair.

Negotium is nominative singular.

Its job is to be the subject of est:

• Hoc negotium grave est = This matter is serious

In other words, negotium is the thing being described.

You can think of the structure like this:

• hoc negotium = subject
• grave = predicate adjective
• est = is

Because grave must agree with negotium, which is neuter singular.

The adjective is from gravis, grave = heavy, serious, weighty.

Its forms include:

• gravis for masculine/feminine singular nominative
• grave for neuter singular nominative

Since negotium is neuter, Latin says:

• negotium grave = a serious matter

not negotium gravis.

Here grave means something like serious, important, or weighty.

Although the basic idea of gravis can be heavy, in many contexts it is used more figuratively:

• grave negotium = a serious matter
• grave periculum = serious danger

So in this sentence, grave does not mean physically heavy. It means that the matter is serious or significant.

Latin word order is much more flexible than English word order.

English usually requires:

• This matter is serious

Latin can say:

• Hoc negotium grave est

and that is completely normal.

The verb often comes later in the sentence, and adjectives can also appear in different positions. Latin endings show the grammatical relationships, so Latin does not rely on word order as heavily as English does.

Iudex is nominative singular, and it is the subject of scit.

So:

• iudex = the judge
• scit = knows

Together:

• iudex veritatem scit = the judge knows the truth

We know iudex is the subject because:

1. its form fits a nominative singular noun,
2. scit is third person singular, so it naturally goes with a singular subject,
3. veritatem is clearly accusative, so that is the direct object instead.

Because veritatem is in the accusative singular, used here as the direct object of scit.

The base noun is:

• veritas = truth

Its accusative singular form is:

• veritatem

So:

• veritas = truth (subject form)
• veritatem = truth (object form)

Since the judge knows the truth, truth is the thing directly affected by the verb, so Latin uses the accusative:

• iudex veritatem scit

Latin does not have articles like English the and a/an.

So a Latin noun by itself can mean:

• a judge
• the judge

depending on context.

That means:

• iudex can mean a judge or the judge
• veritatem can mean truth, the truth, or sometimes a truth, depending on context

In a sentence like this, English usually supplies the:

• the judge knows the truth

But Latin itself does not use separate words for those articles.

Sed means but.

It connects two clauses that are being contrasted:

• Hoc negotium grave est = This matter is serious
• sed iudex veritatem scit = but the judge knows the truth

So the full sentence sets up a contrast or balance:

• the matter is serious,
• but the judge knows the truth.

Sed often appears near the beginning of the second clause, just as but often does in English.

Yes, to a large extent.

Because Latin uses endings to mark grammatical function, several word orders are possible. For example, these would still mean essentially the same thing:

• Hoc negotium grave est, sed iudex veritatem scit.
• Grave est hoc negotium, sed iudex veritatem scit.
• Iudex veritatem scit, sed hoc negotium grave est.

However, different word orders can slightly change the emphasis.

For example:

• Grave est hoc negotium puts more attention on grave
• Veritatem iudex scit puts more attention on veritatem

So the meaning stays basically the same, but the focus can shift.

Here it is an adjective because it directly modifies a noun:

• hoc negotium = this matter

A pronoun would stand by itself, without a noun, as in something like:

• Hoc grave est = This is serious

So in your sentence:

• hoc = demonstrative adjective
• negotium = the noun it describes

Scit is present tense, third person singular.

Its basic dictionary form is:

• scio = I know

So the relevant forms are:

• scio = I know
• scis = you know
• scit = he/she/it knows

Thus:

• iudex veritatem scit = the judge knows the truth

All of those can be reasonable, depending on context.

Negotium has a fairly broad meaning. It can refer to:

• business
• matter
• affair
• task
• problem
• concern

In this sentence, matter or case may sound most natural in English, especially because the second clause mentions a judge. So a learner might understand:

• This matter is serious, but the judge knows the truth.

Even if the meaning has already been given, it is useful to know that negotium is a flexible word whose best English translation depends on context.