Mater genas puellae leniter fricat, quo rubor discedat et puella hilarior fiat.

Because genas is the direct object of fricat.

• fricat = she rubs
• What does she rub? the cheeks

The basic noun is gena, genae (cheek), a first-declension noun. Its accusative plural is genas.

So:

• genae = cheeks as subject
• genas = cheeks as object

Here the mother is doing the action, and the cheeks receive it, so genas must be accusative.

Here puellae is most naturally genitive singular: the girl's.

So genas puellae means:

• the girl's cheeks
• literally, the cheeks of the girl

A learner may notice that puellae could also be dative singular in another sentence, but here the genitive makes sense because it shows possession.

So the structure is:

• Mater = the mother
• genas puellae = the girl's cheeks
• leniter fricat = gently rubs

Leniter is an adverb, meaning gently or softly.

It tells us how the mother rubs the girl's cheeks.

It comes from the adjective lenis (gentle, mild). A very common Latin pattern is:

• adjective → adverb in -ter or -iter

So:

• lenis = gentle
• leniter = gently

Fricat is:

• 3rd person singular
• present tense
• active voice
• indicative mood

from frico, fricare = to rub

So mater ... fricat means:

• the mother rubs
• or mother is rubbing

Since mater is singular, the verb is singular too.

Quo here introduces a purpose clause: in order that, so that.

A very common question is why Latin uses quo instead of the more familiar ut. The main reason is that quo is often used in purpose clauses when there is a comparative in the clause.

And there is a comparative here:

• hilarior = more cheerful

So:

• quo rubor discedat et puella hilarior fiat
• so that the redness may go away and the girl may become more cheerful

In many textbooks you will see the rule stated roughly like this:

• ut
  • subjunctive = purpose
• but quo is often preferred when a comparative appears

They are subjunctive because they are in a purpose clause introduced by quo.

Latin normally uses:

• ut or quo
  • subjunctive
• to express purpose, aim, or intention

So the mother rubs the girl's cheeks for the purpose that:

• rubor discedat = the redness may go away
• puella hilarior fiat = the girl may become more cheerful

The subjunctive here does not mean doubt. It marks the clause as expressing purpose.

Here quo means something like:

• so that
• in order that
• to the end that

It does not mean where in this sentence.

A very literal feeling for the clause is:

• Mother gently rubs the girl's cheeks, so that the redness may go away and the girl may become more cheerful.

So quo is functioning as a conjunction introducing the purpose clause.

Rubor is nominative singular.

It is the subject of discedat.

So the idea is:

• rubor discedat = the redness may depart / go away

The mother is not doing the departing; the redness is. That is why rubor is nominative, not accusative.

Discedat comes from discedo, discedere, which often means:

• go away
• depart
• withdraw

Here rubor discedat means:

• the redness may go away
• the blush may fade

It is a natural metaphor in Latin: the redness departs.

Hilarior is the comparative form of hilaris:

• hilaris = cheerful
• hilarior = more cheerful

The sentence does not just say that the girl becomes cheerful, but that she becomes more cheerful than before.

Because it goes with puella, it is:

• feminine
• nominative singular

This matches the subject puella.

Because fio often means become.

So:

• puella hilarior fiat = the girl may become more cheerful

If Latin used sit instead, that would mean may be rather than may become.

Compare:

• puella hilaris sit = the girl may be cheerful
• puella hilarior fiat = the girl may become more cheerful

So fio emphasizes a change of state.

Fiat is:

• 3rd person singular
• present subjunctive

from fio, fieri

In this sentence it means may become.

Learners often first meet fio as related to facio, but it also has its own common sense of become or happen. Here that independent meaning is the important one.

Because both verbs belong to the same purpose clause.

The mother rubs the girl's cheeks for two connected purposes:

1. quo rubor discedat = so that the redness may go away
2. et puella hilarior fiat = and so that the girl may become more cheerful

Latin often uses one conjunction such as ut or quo to introduce the clause, and then simply connects multiple verbs inside it with et.

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

A useful breakdown is:

• Mater = subject
• genas puellae = object + genitive
• leniter = adverb
• fricat = main verb
• quo ... discedat et ... fiat = purpose clause

So literally it is something like:

• Mother the girl's cheeks gently rubs, so that the redness may go away and the girl may become more cheerful.

A more natural English order is:

• The mother gently rubs the girl's cheeks so that the redness may go away and the girl may become more cheerful.

It can mean redness, blushing, or a blush, depending on context.

In this sentence, since someone is rubbing the girl's cheeks, rubor probably refers to visible redness in the cheeks, perhaps a blush or flushed color.

So a translation might use:

• redness
• the blush
• the flushing

All of those are close to the Latin idea here.

Yes, Latin authors sometimes do use ut for ordinary purpose clauses. But here quo is especially fitting because the clause contains the comparative hilarior.

So:

• ut rubor discedat et puella hilarior fiat would be understandable,

but

• quo rubor discedat et puella hilarior fiat is more idiomatic in the presence of a comparative.

That is why quo is a good choice here.