Non poena, sed praemium pueros saepe laetos facit, et pueri officium suum melius faciunt.

They are nominative because they are the subject words of facit in the first clause.

• poena = punishment
• praemium = reward

The structure non ... sed ... means not ... but ... or not X, but rather Y. So the sentence sets up a contrast:

• Non poena, sed praemium ... facit
  = Not punishment, but reward ... makes ...

Even though both nouns appear, the real positive statement is about praemium, which is why the verb is singular: facit.

Because non poena, sed praemium does not mean punishment and reward. It means not punishment, but reward.

So Latin is not treating this as a compound subject with two things acting together. Instead, it is correcting one idea with another:

• not poena
• but praemium

That means the true subject is effectively praemium, which is singular, so the verb is singular too: facit.

Because the boys have different jobs in the two clauses.

In the first clause:

• praemium pueros saepe laetos facit
• pueros is the direct object of facit
• so it is accusative

In the second clause:

• et pueri officium suum melius faciunt
• pueri is the subject of faciunt
• so it is nominative

So the sentence shifts from reward makes the boys happy to the boys do their duty better.

Because after verbs like facere meaning to make, Latin often uses:

• a direct object in the accusative
• plus another accusative describing what that object becomes

So in:

• pueros laetos facit

Latin literally has something like:

• it makes the boys happy

Both pueros and laetos are accusative because laetos describes the state the boys are made into.

This is often called a predicate accusative or object complement.

Latin word order is flexible, and speakers often move words forward for emphasis.

Putting Non poena, sed praemium first highlights the contrast right away:

• Not punishment, but reward ...

In English we usually rely more on fixed word order, but Latin can use word placement to stress what matters most. Here the sentence wants you to notice the contrast before anything else.

Saepe means often, and it modifies the verb facit.

So:

• praemium pueros saepe laetos facit
• reward often makes boys happy

It tells you how frequently the action happens.

Because Latin adverbs are flexible in position, saepe can sit between other words without changing its basic function.

Because melius here is an adverb, not an adjective.

In the second clause:

• pueri officium suum melius faciunt

the word melius describes how they do their duty:

• better

It modifies the verb faciunt, so an adverb is needed.

If Latin used an adjective like meliores, that would mean better boys or better people, not do better.

Because suus, -a, -um is the reflexive possessive adjective, used when the possession belongs to the subject of the clause.

In the second clause:

• pueri ... officium suum ... faciunt

the subject is pueri, so suum means their own.

Latin uses eorum for their, but usually when it refers to someone other than the subject of that clause.

So:

• suum = their own duty, belonging to the boys who are the subject
• eorum = their duty, belonging to some other group already mentioned

Officium is accusative singular.

That is because it is the direct object of faciunt in the second clause:

• pueri officium suum melius faciunt
• the boys do their duty better

The subject is pueri, the verb is faciunt, and the thing being done is officium suum.

Yes, it is the same verb, facere, but English translates it differently depending on context.

• facit in the first clause = makes
• faciunt in the second clause = do

Latin facere has a wider range than English make. It can mean:

• make
• do
• perform
• cause

So:

• pueros laetos facit = makes the boys happy
• officium suum faciunt = do their duty

Same Latin verb, different natural English translation.

Because classical Latin has no articles.

So a noun like poena can mean:

• punishment
• a punishment
• the punishment

and the exact sense depends on context.

The same is true for:

• praemium = reward / a reward / the reward
• pueri = boys / the boys
• officium = duty / the duty

English requires articles much more often, but Latin does not.

It has two coordinated clauses joined by et.

First clause:

• Non poena, sed praemium = subject
• pueros = direct object
• laetos = object complement / predicate accusative
• facit = verb
• saepe = adverb

So:

• Reward often makes the boys happy

Second clause:

• pueri = subject
• officium suum = direct object
• melius = adverb
• faciunt = verb

So:

• and the boys do their duty better

This is a nice example of Latin showing cause and result across two clauses.