Amica puellae beneficium facit, et puella ei magnas gratias agit.

Because puellae is in the dative singular, meaning to the girl or for the girl.

In the phrase beneficium facit, the person who receives the favor is put in the dative case:

• amica = the friend, as the subject
• puellae = to/for the girl
• beneficium = a kindness, favor

So Amica puellae beneficium facit means that the friend does a favor for the girl.

Literally, beneficium facit means makes/does a kindness or does a favor.

Latin often uses a noun + verb expression where English prefers a single verb. So instead of one simple verb meaning does a favor, Latin commonly says:

• beneficium facere = to do a favor / show kindness

This is a very normal Latin way of speaking. English does something similar in expressions like:

• give thanks
• do harm
• make a mistake

So even if the English meaning is simple, the Latin structure may use a noun with a very common verb like facere.

Here amica is a noun, meaning female friend.

It can also be an adjective in other sentences, meaning friendly or kind, depending on context. But in this sentence it is clearly a noun because it stands on its own as the subject of the first clause:

• Amica ... facit = The female friend ... does

So here amica is not describing another word; it is the person doing the action.

Ei is the dative singular of the pronoun meaning to him, to her, or to it.

In this sentence, it refers back to amica, so it means to her:

• puella ei magnas gratias agit = the girl gives great thanks to her

Latin often uses a pronoun instead of repeating the noun. English does the same:

• The friend does the girl a favor, and the girl thanks her.

One important thing to notice: ei does not itself show gender clearly in form here. It can mean to him, to her, or to it. The context tells you that it means to her.

Because Latin uses the idiom gratias agere, literally to give thanks, with gratias in the accusative plural.

So:

• gratias agit = she gives thanks / she thanks

This is just the normal Latin expression. English also uses thanks as a plural-looking word in many expressions:

• many thanks
• give thanks

So gratias is not unusual here; it is the standard form in this idiom.

Because magnas has to agree with gratias.

Here:

• gratias is accusative plural feminine
• so the adjective must also be accusative plural feminine
• therefore: magnas

So:

• magnas gratias agit = she gives great thanks or more naturally she thanks her very much

This is a good example of adjective agreement in Latin: adjectives match the noun they describe in gender, number, and case.

Here is the breakdown:

First clause

Amica puellae beneficium facit

• Amica = subject, the friend
• puellae = indirect object, to/for the girl
• beneficium = direct object, a favor
• facit = verb, does/makes

Second clause

et puella ei magnas gratias agit

• puella = subject, the girl
• ei = indirect object, to her
• magnas gratias = direct object, great thanks
• agit = verb, gives/does

So the sentence neatly reverses the roles:

• first, the friend helps the girl
• then, the girl thanks the friend

Because Latin often shows meanings like to or for by using a case ending, not a separate word.

That is what the dative case does here:

• puellae = to/for the girl
• ei = to her

English usually needs a preposition like to, but Latin often does not. Instead, the ending itself tells you the function of the word.

So a learner should get used to thinking:

• -ae here = dative singular
• ei here = dative pronoun

rather than looking for a separate word meaning to.

Because Latin word order is much more flexible than English word order.

English depends heavily on position:

• The friend helps the girl is different from
• The girl helps the friend

Latin depends much more on endings than on position. So in this sentence, you know who is doing what mainly because of the cases:

• amica = nominative subject
• puellae = dative
• beneficium = accusative object

That means Latin can move words around for emphasis or style without changing the core meaning.

For example, the first clause could also appear as:

• Puellae amica beneficium facit
• Beneficium amica puellae facit

The endings still tell you the grammatical roles.

Not by itself.

The basic meaning of agere is something like to drive, to do, to act, or to conduct, depending on context. But in the fixed expression gratias agere, it means to give thanks or simply to thank.

So:

• agit alone does not mean thanks
• gratias agit together means gives thanks / thanks

This is another idiomatic expression that you should learn as a whole phrase.

Yes. Even if the meaning is already known, it helps to see how Latin expressions map into natural English.

Possible natural translations include:

• The friend does the girl a favor, and the girl thanks her.
• A friend does a favor for the girl, and the girl gives her many thanks.
• The girl’s friend does her a kindness, and the girl thanks her warmly.

The exact English wording can vary, because Latin idioms like beneficium facere and gratias agere do not always match one English verb exactly word-for-word.