Epistula matris puellam laetam facit.

Because epistula is in the nominative singular, which is the case typically used for the subject.

Here the basic structure is:

• epistula = the subject
• facit = the verb
• puellam laetam = what is being affected by the verb

So epistula is the thing doing the action of facit.

Matris is the genitive singular form of mater, meaning of the mother or the mother's.

So:

• mater = mother
• matris = of the mother

In epistula matris, the genitive shows possession: the mother's letter.

Because facere can mean to make in the sense of to cause someone/something to be a certain way.

In that pattern:

• the person affected goes into the accusative
• the adjective describing the result also agrees with that noun

So:

• puellam = the girl, as direct object
• laetam = happy, describing puellam

Latin is doing something like:

• The letter makes the girl happy

That is why both words are feminine singular accusative.

Adjectives in Latin agree with the nouns they describe in:

• gender
• number
• case

Since puellam is:

• feminine
• singular
• accusative

laetam must also be:

• feminine
• singular
• accusative

This agreement shows that laetam describes puellam, not epistula or matris.

Facit is from facere, which can mean:

• to do
• to make

In this sentence it means makes in the causative sense:

• makes the girl happy

So the pattern is:

• subject
  • facit
    • object
      • resulting description

That is a very common Latin construction.

No. The forms do not match.

• epistula is nominative singular feminine
• laetam is accusative singular feminine

Since laetam is accusative, it matches puellam, which is also accusative singular feminine.

If the adjective described epistula, you would expect laeta, not laetam.

Latin usually does not use articles like English the or a/an.

So epistula can mean:

• a letter
• the letter

And puellam can mean:

• a girl
• the girl

You decide which is most natural from the context.

Yes. Latin word order is much more flexible than English because the endings show each word’s role.

So all of these could express the same basic idea:

• Epistula matris puellam laetam facit
• Puellam epistula matris laetam facit
• Matris epistula puellam laetam facit

However, word order can affect emphasis. The original order is a normal, clear way to present the sentence.

Matris is genitive singular.

The genitive often shows:

• possession
• relationship
• description

Here it tells you whose letter it is:

• epistula matris = the mother's letter

So matris is dependent on epistula.

They come from different declensions:

• epistula, epistulae = 1st declension
• mater, matris = 3rd declension
• puella, puellae = 1st declension

That is why their endings are different:

• epistula = nominative singular
• matris = genitive singular
• puellam = accusative singular

A learner often expects all feminine nouns to decline alike, but Latin nouns are grouped by declension, not just by gender.

Here matris is genitive singular: of the mother.

It is not plural. The genitive plural of mater would be matrum.

So:

• matris = of the mother
• matrum = of the mothers

That helps confirm that the sentence refers to one mother.

Because its subject, epistula, is singular.

• epistula = one letter
• facit = it makes

If the subject were plural, the verb would normally be plural too. For example, epistulae ... faciunt would mean letters make...