Plerique liberi laeti sunt, quia iter facere amant.

Plerique means most or the majority of. It is agreeing with liberi, so it is nominative masculine plural.

A learner might expect something more like multi for many, but plerique is specifically most rather than just many.

Liberi is nominative plural, because it is the subject of the sentence.

The sentence is about the children, and the verb sunt means are, so liberi is the thing being described as happy.

They are both describing liberi, so they must agree with it in number, gender, and case.

• liberi = plural
• plerique = plural
• laeti = plural

This is a basic Latin agreement pattern: adjectives match the nouns they describe.

Not necessarily. Latin often uses the masculine plural for a group that is mixed or unspecified.

So liberi can mean children in general, and laeti agrees with that grammatical form. It does not have to mean the group is only male.

Sunt is the verb are. Latin often uses forms of sum to link a subject with an adjective:

• liberi laeti sunt = the children are happy

Here laeti is a predicate adjective, and sunt connects it to the subject.

Because Latin verb endings already show who is doing the action.

• amant = they love
• sunt = they are

So Latin often does not need an extra subject pronoun like they unless it is being emphasized.

Quia means because. It introduces a reason clause.

So the sentence has:

• main clause: Plerique liberi laeti sunt
• reason clause: quia iter facere amant

The second clause explains why they are happy.

Because it goes with amant.

Latin, like English, can use an infinitive after a verb such as love:

• amant facere = they love to do
• amant iter facere = they love to travel / make a journey

So iter facere acts as the thing they love doing.

Iter is accusative singular, the direct object of facere.

The full phrase is iter facere, literally something like to make a journey, but naturally to travel.

It may look unchanged because iter is a neuter third-declension noun, and its nominative singular and accusative singular are both iter.

Yes. It is a common Latin idiom meaning to travel, to go on a journey, or to make a journey.

A native English speaker might try to translate each word separately, but the phrase works as a single expression. So it is better to learn iter facere together.

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

For example, Latin could also put the quia clause first for emphasis:

• Quia iter facere amant, plerique liberi laeti sunt.

That would still mean the same basic thing: Most children are happy because they love to travel.

No. Depending on context, liberi can have other meanings, especially forms related to free.

But in this sentence, the meaning is clearly children. Context and the given translation tell you which meaning is intended.