Pater mihi consilium dat, et ego eo libenter utor.

Because mihi is the indirect object: it names the person to whom something is given.

With dare (to give), Latin normally uses:

• the thing given in the accusative
• the recipient in the dative

So in Pater mihi consilium dat:

• pater = the father, the giver
• consilium = the advice/counsel, the thing given
• mihi = to me, the recipient

So mihi is the dative singular of ego.

Because it is the direct object of dat.

The verb dat means he gives, and the thing being given is consilium. That makes consilium the direct object, so it appears in the accusative singular.

A very common pattern with dare is:

• someone gives
• something to someone

In Latin:

• something = accusative
• to someone = dative

So:

• consilium = accusative
• mihi = dative

Here eo is a form of the pronoun is, ea, id, meaning it.

It refers back to consilium. So eo ... utor means I use it.

More specifically, eo is:

• ablative singular
• masculine or neuter

Since consilium is neuter singular, eo matches it.

So the second half literally works like:

• et ego eo libenter utor = and I use it gladly/willingly

Because the verb utor takes the ablative, not the accusative.

This is something learners simply have to get used to: some Latin verbs govern cases that do not match what English speakers expect.

So although English says I use it, Latin says:

• utor
  • ablative

That is why Latin has eo utor, not eum utor or id utor.

This is one of the most important things to remember about utor:

• utor, uti, usus sum = to use
• it takes an ablative object

Because utor is a deponent verb.

Deponent verbs:

• have passive-looking forms
• but active meanings

So utor looks like a passive form, but it means I use, not I am used.

In this sentence:

• utor = I use
• not I am used

This is completely normal for deponent verbs in Latin.

Yes. The ending of utor already tells you the subject is I.

So Latin could simply say:

• et eo libenter utor

The pronoun ego is added for emphasis or contrast. It helps bring out the idea:

• Father gives me advice, and I, for my part, gladly use it.

So ego is not required for grammar, but it adds stress or clarity.

Libenter is an adverb meaning gladly, willingly, or with pleasure.

It modifies utor, so it tells you how the speaker uses the advice:

• I use it gladly

Its position is flexible. Latin word order is freer than English word order, so libenter can often be moved without changing the basic meaning.

Here eo libenter utor is a natural way to say:

• I gladly use it

Not in the same rigid way it is in English.

Latin uses endings to show grammatical function, so word order is often used more for emphasis, style, or flow than for basic meaning.

In this sentence:

• Pater is nominative, so it is the subject
• mihi is dative, so it is the recipient
• consilium is accusative, so it is the thing given
• eo is ablative with utor

So even if the order changed, the endings would still show the relationships.

For example, Latin could also say something like:

• Pater consilium mihi dat
• Et ego libenter eo utor

The meaning would stay essentially the same.

Yes, at first glance it can be confusing, because eo can also be the first-person singular of ire (I go).

But here the context makes it clear that eo is the pronoun it, not the verb I go.

Why?

• If eo meant I go, then et ego eo libenter utor would not make sense.
• Also, utor needs an ablative object, and eo fits that perfectly as the ablative of is, ea, id.

So in this sentence, eo definitely means with it / it.

Both are present tense.

• dat = he gives
• utor = I use

So the sentence describes a present or habitual action:

• Father gives me advice, and I gladly use it or
• My father gives me advice, and I gladly follow/use it

Latin present tense can often cover both a simple present idea and a habitual one, depending on context.

Because Latin has no articles.

Unlike English, Latin does not have words that directly correspond to a, an, or the. So:

• pater can mean father, the father, or a father
• consilium can mean advice, the advice, a plan, and so on

The exact sense depends on context.

So when reading Latin, you have to supply a/an/the naturally in English based on what makes sense in the sentence.