Puer rogat utrum melius sit aquam an lac cum farina miscere, sed coquus respondet se iam satis scire.

Utrum ... an is a standard Latin way to set up an either/or question. It means whether ... or.

So:

• utrum ... aquam an lac ... = whether ... water or milk ...

In English we often say whether water or milk is better, and Latin uses utrum ... an to mark those two alternatives clearly.

Because this is an indirect question.

The boy is not asking the question directly in the sentence. Instead, the sentence says:

• Puer rogat ... = The boy asks ...

After a verb like asks, Latin normally puts the verb of the indirect question into the subjunctive. So:

• direct question: quid melius est? = what is better?
• indirect question: rogat quid melius sit = he asks what is better

Here the same rule gives:

• utrum melius sit ... = whether it is better ...

Melius is the neuter singular comparative form of bonus used adverbially or impersonally, and here it means better.

Latin often says:

• melius est/sit + infinitive = it is better to ...

So:

• melius sit aquam an lac cum farina miscere = whether it is better to mix water or milk with flour

The neuter form melius is used because the idea is impersonal: it is better.

Because they are the direct objects of miscere.

The verb miscere means to mix, and the things being mixed are put in the accusative:

• aquam miscere = to mix water
• lac miscere = to mix milk

So in this sentence the question is about whether it is better to mix:

• aquam cum farina = water with flour
• lac cum farina = milk with flour

Because lac is a neuter third-declension noun, and its nominative singular and accusative singular are the same:

• nominative: lac
• accusative: lac

So even though it is the direct object, the form stays lac.

Its other forms show the stem more clearly, for example:

• genitive: lactis

That is why English speakers often expect something like lactem, but Latin does not form it that way.

Because it depends on melius sit in the construction:

• melius est/sit + infinitive = it is better to ...

So Latin is literally saying something like:

• the boy asks whether it may be better to mix water or milk with flour

The infinitive miscere expresses the action being evaluated.

The preposition cum takes the ablative case, so:

• cum farina = with flour

That is why the noun appears as farina, the ablative singular form.

So:

• aquam cum farina miscere = to mix water with flour
• lac cum farina miscere = to mix milk with flour

This is an indirect statement (also called an accusative-and-infinitive construction).

After verbs of saying, thinking, answering, perceiving, and similar ideas, Latin often uses:

• accusative subject + infinitive

Here:

• respondet = he replies
• se = that he
• scire = to know

So:

• coquus respondet se iam satis scire = the cook replies that he already knows enough

Latin does this where English usually uses that + finite verb.

Because se is the reflexive accusative pronoun, and it refers back to the subject of the main verb.

The main clause subject here is:

• coquus = the cook

So:

• coquus respondet se iam satis scire = the cook replies that he himself already knows enough

If Latin used eum, that would normally refer to some other male person, not back to coquus.

This is a very common pattern in indirect statement:

• Marcus dicit se venire = Marcus says that he is coming

Here se refers to Marcus.

It means to know enough already.

• iam = already / by now
• satis = enough
• scire = to know

So the cook is saying that he already has sufficient knowledge; in context, it means he already knows what is needed about the matter.

Latin often leaves the object of scire understood from context, just as English can say:

• I know enough already

without repeating about this or what to do.

No, satis is an indeclinable word meaning enough.

It can function a bit like an adverb or as a substantive idea of sufficiency, depending on context. In this sentence it works naturally as:

• satis scire = to know enough

So you do not look for agreement with another noun the way you would with a normal adjective.

The case endings and verb forms tell you.

• Puer is nominative singular: the boy → subject of rogat
• rogat = asks
• aquam = accusative singular: water → object of miscere
• lac = accusative singular form: milk → alternative object of miscere
• farina after cum is ablative: with flour
• coquus is nominative singular: the cook → subject of respondet
• se is accusative: subject of the infinitive scire in indirect statement

So the structure is:

• The boy asks whether it is better to mix water or milk with flour
• but the cook replies that he already knows enough

It is normal Latin word order: flexible, but meaningful.

Latin does not depend on word order as strictly as English because the endings show the grammar. Still, the order helps organize the sentence:

• Puer rogat gives the main action first
• utrum ... an ... introduces the alternatives
• miscere comes at the end of its clause, which is very common in Latin
• sed coquus respondet introduces the contrast
• se iam satis scire places the indirect statement after respondet

A very literal ordering would sound odd in English, but in Latin it is natural and clear.