Mater respondet solacium bonorum verborum infelicibus valde necessarium esse.

The sentence has two parts:

• Mater respondet = the main clause
• solacium bonorum verborum infelicibus valde necessarium esse = what the mother replies

So structurally it is:

• Mother replies
• that ...

Latin often uses this kind of setup after verbs of saying, thinking, knowing, hearing, and replying.

Because Latin usually does not use a conjunction like English that after verbs such as respondet.

Instead, it uses an indirect statement construction:

• a subject in the accusative
• plus an infinitive

Here that construction is:

• solacium ... esse

In natural English, we usually translate it with that:

• Mother replies that ...

But in Latin, the that is built into the grammar of the accusative + infinitive construction.

Esse is the present infinitive of sum, meaning to be.

It is needed because the indirect statement says that something is very necessary:

• solacium ... necessarium esse = that comfort ... is necessary

As for position: Latin word order is flexible, but infinitives like esse very often come near the end of the clause. So this placement feels very normal.

Excellent question. Solacium is accusative singular here, even though it looks identical to the nominative.

That happens because solacium is a neuter second-declension noun, and for neuter nouns:

• nominative singular = accusative singular

So:

• nominative: solacium
• accusative: solacium

In this sentence it is accusative because it is the subject of the indirect statement after respondet.

Because in Latin indirect statement, the subject is put in the accusative, not the nominative.

English says:

• Mother replies that the comfort is necessary

Latin says, more literally:

• Mother replies the comfort to be necessary

So the subject inside that reported statement, solacium, becomes accusative.

This is one of the most important Latin constructions to learn: the accusative-and-infinitive construction.

Because it agrees with solacium.

Solacium is:

• neuter
• singular
• accusative

So the adjective that goes with it must match:

• necessarium = neuter singular accusative

That is why it is necessarium, not necessarius or necessaria.

Bonorum verborum is a genitive plural phrase:

• verborum = of words
• bonorum = of good / good, agreeing with verborum

So solacium bonorum verborum means something like:

• the comfort of good words
• the comfort that comes from good words
• the comfort provided by kind words

This genitive tells you what kind of comfort is meant, or where the comfort comes from.

Because necessarius commonly takes the dative of the person for whom something is necessary.

So:

• alicui necessarius = necessary for someone

Here:

• infelicibus = for the unhappy people / for the unfortunate

So:

• valde necessarium infelicibus = very necessary for the unhappy

Because the sentence is talking about unhappy people in general, not one specific unhappy person.

Infelicibus can be masculine or feminine dative/ablative plural, depending on context. Here it means something like:

• for unfortunate people
• for the unhappy

If the sentence meant for an unhappy person, you would expect a singular form such as infelici.

Valde modifies necessarium.

So the sense is:

• very necessary

It is an adverb strengthening the adjective.

A learner sometimes wonders whether it could mean greatly in some other way, but here the straightforward reading is simply:

• very necessary

Because valde is the normal adverb for strengthening an adjective or another adverb:

• valde necessarium = very necessary

Multum can sometimes be used adverbially, but valde is the more standard choice here for plain intensification.

Yes. Latin word order is much freer than English word order because the endings show the grammatical relationships.

For example, the core relationships would stay the same even if the order changed. But the given order is quite natural:

• Mater respondet first gives the main action.
• solacium bonorum verborum presents the thing being discussed.
• infelicibus adds who it is necessary for.
• valde necessarium esse finishes the indirect statement with the predicate and infinitive.

Putting esse at the end is especially common.

It could mean several closely related things, depending on context:

• good
• kind
• helpful
• beneficial

So bonorum verborum could be understood as:

• good words
• kind words
• comforting words

Latin bonus is often broader than a single English word, so context helps decide the best nuance.

You should understand the Latin grammar literally, but you do not always have to translate it literally.

Grammatically, it is indeed:

• comfort of good words

But in smoother English, that often becomes something like:

• the comfort of kind words
• the comfort that kind words bring
• the consolation of good words

So the Latin structure is genitive, but the best English phrasing may vary.