Pater servum iubet equum ad arborem ligare.

They are both accusative, but they do different jobs.

• servum is the object of iubet: the father orders the slave
• equum is the object of ligare: to tie the horse

This is a very common Latin pattern with iubeo:

iubeo + person in the accusative + infinitive

So Latin can have one accusative with the main verb and another accusative with the infinitive.

The one doing the tying is servum.

With iubeo, the person ordered is usually the understood subject of the infinitive. So the structure is:

• father orders the slave
• to tie the horse

In other words, the slave is the one who performs ligare.

Ligare is an infinitive, and the Latin infinitive already includes the idea of English to.

So:

• ligare = to tie

Latin does not need a separate word for to here. English says to tie with two words; Latin says ligare with one.

Because iubeo normally takes an infinitive construction, not an ut clause.

The usual pattern is:

• iubeo aliquem facere aliquid
• I order someone to do something

So servum ... ligare is exactly what you would expect after iubet.
For an English speaker, it may help to think:

• English: orders the slave to tie
• Latin: orders the slave tie-to

That is not literal English, of course, but it shows why the infinitive is there.

Ad takes the accusative case, so arborem must be accusative.

Here ad arborem means to the tree in the sense of to/against/onto the tree as the place of fastening. With ligare, it means the horse is being tied to the tree.

So:

• ad + accusative = direction toward, position against, or attachment to something

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

So:

• pater can mean father, the father, or a father
• servum can mean a slave or the slave
• equum can mean a horse or the horse

The context tells you which English translation is best.

Yes. Latin word order is more flexible than English word order because the endings show the grammatical roles.

This sentence is a normal and clear order:

Pater servum iubet equum ad arborem ligare.

But Latin could move words around for emphasis. Even so, some arrangements sound more natural than others. Here it is helpful that:

• servum stands near iubet, showing who is being ordered
• equum ad arborem ligare stays together as the action commanded

So the order is not random, even though Latin is flexible.

Mainly from the construction of iubeo.

With iubeo, the normal pattern is:

• person ordered = accusative right after or near iubeo
• action ordered = infinitive phrase
• any object inside that infinitive phrase belongs to the infinitive

So:

• servum belongs with iubet
• equum belongs with ligare

That is why the sentence means that the slave is ordered, and the horse is tied.

Here are the main forms a learner would usually look up:

• pater from pater, patris = father
• servum from servus, servi = slave
• iubet from iubeo, iubere, iussi, iussum = order
• equum from equus, equi = horse
• ad = to, toward, at, against
• arborem from arbor, arboris = tree
• ligare from ligo, ligare, ligavi, ligatum = tie, bind

Iubet is present tense: he orders or he is ordering.

Ligare is a present infinitive. After iubet, it usually refers to an action that is to happen as part of that command, without separately marking it as past or future.

So the sense is simply that the father gives an order for the slave to tie the horse.