Ante cenam puella breve exercitium scribendi facit, et mater ei verba nova explicat.

It helps to split it into two clauses:

1. Ante cenam puella breve exercitium scribendi facit

   • puella = the subject
   • facit = the verb
   • breve exercitium scribendi = the thing she does
   • ante cenam = a time phrase, before dinner

2. et mater ei verba nova explicat

   • mater = the subject
   • explicat = the verb
   • verba nova = the direct object, the thing being explained
   • ei = the indirect object, to her

So the sentence is built very regularly, even if the word order is not exactly like English.

Because ante is a preposition that takes the accusative when it means before in time or place.

So:

• cena = dinner
• cenam = accusative singular
• ante cenam = before dinner

This is just something you learn with the preposition: ante + accusative.

Latin does not have articles like English the and a/an.

So:

• puella can mean girl, a girl, or the girl
• mater can mean mother, a mother, or the mother
• verba nova can mean new words or the new words, depending on context

English has to choose an article, but Latin usually leaves that to context.

Because the adjective has to agree with the noun it describes.

• exercitium is neuter singular
• Therefore the adjective must also be neuter singular
• The neuter singular form of brevis is breve

So:

• brevis puella would be wrong anyway because brevis means short, not small
• breve exercitium = a short exercise

This is a standard third-declension adjective agreement pattern.

scribendi is the gerund, specifically the genitive singular of scribere (to write).

Here it depends on exercitium:

• exercitium scribendi = literally an exercise of writing
• More naturally in English: a writing exercise

So scribendi does not mean a person doing the writing. It is a verbal noun form, used to express the activity itself.

Because the meaning is not simply she writes. It is more specifically she does a writing exercise.

• scribit = she writes
• exercitium scribendi facit = she does a writing exercise

Latin often uses facere with exercitium in the same way English uses do with exercise.

ei is dative singular, meaning to her or for her.

In this sentence:

• mater ei verba nova explicat = mother explains new words to her

The person receiving the explanation is in the dative.

If you used eam, that would be accusative, meaning her as a direct object, which would not fit the structure here.

So:

• ei = to her
• eam = her

Because verbum is a neuter noun.

Its accusative plural is:

• verba

And the adjective must agree with it:

• nova = neuter plural

So:

• verba nova = new words

If the noun were masculine plural, then you would get something like novos. But verbum is neuter, so the forms are verba nova.

explicat takes:

• a direct object = the thing explained
• an indirect object = the person to whom it is explained

So here:

• verba nova = what is explained
• ei = to whom it is explained

This is very similar to English:

• She explains new words to her

Latin just shows the roles more clearly by case endings.

Again, Latin usually does not use articles, and it often leaves possession to context if it is obvious.

So mater can mean:

• mother
• the mother
• her mother

In a sentence about a girl and then mater, a reader will naturally understand her mother unless the context suggests otherwise.

Latin does have possessives like sua mater, but it does not always need them.

Yes, this is a normal Latin word order, but Latin word order is much freer than English word order because the case endings show the grammatical roles.

This order is quite natural:

• Ante cenam first gives the time setting
• facit and explicat come at the ends of their clauses, which is very common in Latin

A Latin author could rearrange parts of the sentence for emphasis, for example putting breve or ei in a more prominent position, and the sentence would still make sense.

So word order in Latin often shows emphasis and style more than basic grammar.