Sic in domo, ubi tablinum, triclinium, et peristylium inter se differunt, etiam pueri paulatim discunt quid in his locis recte faciendum sit.

With in, Latin usually uses:

• in + ablative for location: in the house
• in + accusative for motion toward: into the house

So in domo means in the house, which is why the ablative is used.

As for domo: the noun is domus, and it has some irregular forms. Its ablative singular is domo. The same location idea appears later in in his locis, where locis is also ablative.

Here ubi means where or in which. It refers back to domo and introduces a clause describing the house:

in a house where the tablinum, triclinium, and peristylium differ from one another

So this ubi is not mainly temporal (when), but locative (where).

Because all three nouns together form a compound subject. In English we do the same thing:

The kitchen, dining room, and garden are different.

Each noun is singular, but taken together they are plural, so Latin uses differunt = they differ.

Inter se means among themselves or, more naturally in English, from one another / from each other.

So inter se differunt means:

• they differ from one another
• they are different from each other

This is a very common Latin way to express reciprocal difference.

Latin word order is flexible, so etiam often appears near the word it emphasizes. Here it most naturally emphasizes pueri:

etiam pueri = even the children

In other contexts etiam can mean also, but here even is the better sense, because the point is that not just adults, but even children, learn this.

Paulatim means gradually, little by little, or step by step. It modifies discunt.

So paulatim discunt means:

• they gradually learn
• they learn little by little

This suggests a process, not a sudden realization.

Because quid here is the interrogative pronoun what, introducing an indirect question after discunt:

they learn what ...

That is different from quod, which is usually:

• a relative pronoun: which
• or a conjunction: because / that

So quid is exactly what Latin normally uses for what in an indirect question.

Because Latin uses the subjunctive in indirect questions.

The direct question would be:

quid in his locis recte faciendum est?
What should properly be done in these places?

After a verb like discunt (they learn), Latin turns that into an indirect question:

quid in his locis recte faciendum sit

So est becomes sit. Since the main verb discunt is present, the present subjunctive sit is the expected form.

This is a gerundive + esse construction, often called the passive periphrastic. It expresses what ought to be done, should be done, or is to be done.

So:

faciendum sit = should be done / ought to be done

That makes quid in his locis recte faciendum sit mean:

what should properly be done in these places

The form faciendum is neuter singular, matching the general what idea expressed by quid.

Recte is an adverb meaning properly, correctly, or rightly. It modifies the verbal idea faciendum sit, not the noun locis.

So the sense is:

what should be done properly in these places

not:

what should be done in these proper places

They are all neuter singular nouns. In this sentence, each one is in the nominative singular, and many neuter nouns of this type end in -um.

So their endings are not random; they show their grammatical form. That is one clue helping you see that these three nouns are the subject of differunt.