Sedecim verba nova in hoc libello sunt, et magistra vult ut discipuli sedecim ex eis memoria teneant.

Verba is the nominative plural of verbum, meaning word.

Because the sentence is saying sixteen new words are in this little book, verba is the subject of sunt. Since verbum is a neuter noun, its nominative plural ends in -a, so:

• verbum = word
• verba = words

That is why it is verba, not something like verbi.

Because adjectives in Latin must agree with the nouns they describe in gender, number, and case.

So:

• verba = neuter plural nominative
• nova = neuter plural nominative

Together, verba nova means new words.

Even though nova looks like a feminine singular form in some contexts, here it is clearly neuter plural because it agrees with verba.

Hoc libello is ablative singular.

That is because in takes the ablative when it means in or on in the sense of location:

• in hoc libello = in this little book

If in meant motion into something, it would usually take the accusative instead.

Also:

• hoc = ablative singular of hic, haec, hoc (this)
• libello = ablative singular of libellus

Libellus literally means little book or booklet. It is a diminutive of liber.

So in hoc libello is more literally:

• in this little book
• or in this booklet

Depending on context, English may simply translate it as in this book, but the Latin form does carry the idea of smallness.

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

So Latin can say:

• Sedecim verba nova in hoc libello sunt

rather than forcing a strict English-style order such as:

• Sedecim verba nova sunt in hoc libello

Both would be understandable in Latin, but the version in your sentence is perfectly natural. Often Latin places the verb later in the clause.

So this is not a special grammar point so much as a normal feature of Latin style.

Because Latin often uses ut + subjunctive after a verb like vult when one person wants someone else to do something.

Here:

• magistra vult = the teacher wants
• ut discipuli ... teneant = that the students hold/remember ...

So the structure is literally:

• the teacher wants that the students remember ...

In English, we usually say:

• the teacher wants the students to remember ...

Latin often prefers a clause with ut here rather than the English-style infinitive construction.

Teneant is subjunctive because it is inside the ut-clause after vult.

This is a very common Latin pattern:

• a verb of wanting, ordering, advising, etc.
• followed by ut
• followed by a subjunctive verb

So:

• vult ut ... teneant = she wants ... to remember

Also, teneant is plural because its subject is discipuli.

Teneant is the present active subjunctive, third person plural of teneo, tenere.

Breaking that down:

• teneo = I hold / keep
• teneant = they may hold / they should hold / that they hold

In this sentence, because of the ut clause after vult, it is best understood as:

• that they keep
• or more naturally here, that they remember

Literally, memoria teneant means something like:

• they hold in memory
• they keep in memory

This is an idiomatic Latin way to say:

• they remember
• they learn by heart
• they memorize

So memoria tenere is a useful expression to learn as a whole.

Memoria here is ablative singular.

In the expression memoria tenere, Latin uses memoria without a preposition. You can think of it as an idiomatic ablative: to hold by memory / in memory.

So although English would usually need a phrase like in memory, Latin can simply say:

• memoria tenere

This is one of those expressions that is best learned as a set phrase.

Ex eis means out of them or from among them.

Here, eis refers back to verba nova — the new words.

So:

• sedecim ex eis = sixteen of them

Also, ex takes the ablative case, so eis is ablative plural here.

Because discipuli is the subject of teneant inside the ut-clause.

In English, we say:

• the teacher wants the students to remember

and the students looks like the object of wants.

But Latin structures it differently:

• the teacher wants that the students remember

So inside that subordinate clause, discipuli is doing the action of teneant, which means it must be nominative.

Because sedecim is an indeclinable numeral. That means its form does not change for case, gender, or number.

So Latin uses sedecim in both places:

• sedecim verba = sixteen words
• sedecim ex eis = sixteen of them

Many Latin numerals from this range behave this way.

Yes, ex eis already refers to the words, but the repetition of sedecim makes the meaning explicit:

• there are sixteen new words
• the teacher wants the students to remember sixteen of them

In context, that means all sixteen. Latin often repeats information like this for clarity rather than leaving it to implication.