Mater hodie panem domi facere vult, itaque ancillam iubet far ex arca ferre.

Because panem is the accusative singular, and it is the direct object of facere.

• panis = bread as a dictionary form / subject form
• panem = bread as the thing being made

So panem facere means to make bread.

domi is a special form called the locative, used with domus to mean at home.

This is one of the small set of place expressions that Latin handles differently:

• domi = at home
• domum = homeward / to home
• domo = from home

So panem domi facere means to make bread at home.

Because vult means wants, and Latin commonly uses a complementary infinitive after verbs like want, be able, ought, begin, and so on.

So:

• vult = she wants
• facere = to make

Together: vult facere = she wants to make

This works much like English.

ancillam is accusative because it is the person being ordered by iubet.

With iubere, Latin often uses:

• the person ordered in the accusative
• plus an infinitive for what that person is told to do

So:

• ancillam iubet = she orders the slave-girl
• far ... ferre = to bring the grain

Altogether: she orders the slave-girl to bring the grain.

Because it depends on iubet.

Latin often uses this pattern with iubere:

• someone in the accusative
• infinitive for the action ordered

So ancillam ... ferre means the slave-girl to bring.

This is very similar to English:

• She orders the slave-girl to bring...

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

Its basic forms are:

• nominative singular: far
• genitive singular: farris

Since it is the direct object of ferre, it is accusative singular, but for this noun that form is still far.

Because the preposition ex takes the ablative.

• ex = out of / from
• arca is the ablative singular of arca

So ex arca means out of the box/chest or from the chest.

itaque means and so, therefore, or so. It connects the two parts of the sentence by showing result:

• Mother wants to make bread today at home
• therefore / and so she orders the slave-girl to bring the grain

So it signals a logical step from desire to action.

Because Latin has no articles.

So a noun like mater can mean:

• mother
• a mother
• the mother

The exact sense depends on context. The same is true for panem, ancillam, arca, and far.

Because domi expresses place, and the most natural thing it modifies here is the action facere.

So the sense is:

• to make bread at home

It does not describe bread itself; it describes where the making happens.

Latin word order is flexible, so you often decide this by meaning and grammar rather than by position alone.

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

This sentence is arranged in a very natural Latin way:

• Mater — topic/subject first
• hodie — time
• panem domi facere — the action wanted
• vult — main verb of the first clause
• itaque — connection to the next clause
• ancillam — person ordered
• iubet — main verb of the second clause
• far ex arca ferre — the action ordered

Latin often places infinitives and objects before the finite verb, especially in straightforward prose.

Because each belongs to a different main verb:

• vult facere = wants to make
• iubet ... ferre = orders ... to bring

So the sentence contains two separate verb-ideas:

1. what the mother wants to do
2. what she orders the slave-girl to do

That is why both infinitives are needed.

Yes. ferre is an irregular verb meaning to carry or to bring.

Its principal parts are:

• fero
• ferre
• tuli
• latum

In this sentence, ferre means to bring/carry the grain out of the chest.

It is a very common verb, so it is worth learning early.

Yes. facere basically means to make or to prepare. So panem facere can mean to make bread in a general sense.

If Latin specifically wanted to emphasize cooking or baking, other verbs might be used in other contexts. Here the focus is simply that the mother wants bread made, and therefore she has the grain brought out.