Hoc vitrum tam fragile est ut mater infantem id tangere non sinat.

Hoc means this and is neuter nominative singular here, agreeing with vitrum.

• vitrum is a neuter singular noun.
• Since vitrum is the subject of est, hoc must also be nominative.
• So hoc vitrum = this glass.

You could also think of hoc as pointing to something nearby: this glass here.

Vitrum is simply a neuter noun in Latin. Its gender is part of the word and must be learned with the vocabulary.

Because it is neuter:

• adjectives describing it must be neuter too
• pronouns referring to it must also be neuter

That is why you get:

• hoc vitrum
• fragile
• id

all in neuter singular form.

Because fragile has to agree with vitrum, which is neuter singular.

The adjective is fragilis, fragile:

• masculine/feminine nominative singular: fragilis
• neuter nominative singular: fragile

So:

• vir fragilis = a fragile man
• femina fragilis = a fragile woman
• vitrum fragile = a fragile glass

Tam ... ut is a very common Latin pattern meaning so ... that.

In this sentence:

• tam fragile est = is so fragile
• ut ... non sinat = that ... does not allow

So the structure is:

• tam = so
• ut = that

This is called a result clause: the second part gives the result of the first part.

Because after tam ... ut, Latin normally uses the subjunctive in a result clause.

So sinat is present subjunctive of sinere (to allow, permit).

This does not necessarily make the idea doubtful or hypothetical in English. It is just the normal Latin grammar after tam ... ut.

So:

• est = is
• ut ... sinat = that ... allows / would allow / does allow, depending on context and translation style

Because the ut already introduces the whole result clause. The negative non simply negates the verb inside that clause.

So:

• ut mater infantem id tangere non sinat = that the mother does not allow the child to touch it

In result clauses, you will often see the negative expressed with non.

Because mater is the subject of sinat.

It is the mother who is doing the not-allowing.

So the clause works like this:

• mater = subject
• infantem = person being prevented
• tangere = infinitive, the action
• id = object of tangere

In other words: the mother does not allow the child to touch it.

Because sinere often takes:

• a direct object naming the person allowed or prevented
• an infinitive naming the action

So:

• mater infantem tangere non sinat = the mother does not allow the child to touch

Here infantem is the person being allowed or not allowed, so it is in the accusative.

This is similar to English allow someone to do something.

Because after sinere, Latin commonly uses an accusative + infinitive pattern:

• someone in the accusative
• the action in the infinitive

So:

• infantem ... tangere = the child to touch

This is normal after verbs of allowing, ordering, forcing, and similar ideas.

Id means it and refers back to hoc vitrum.

It is:

• neuter singular
• accusative, because it is the object of tangere

Why not hoc again? Because Latin often uses is, ea, id as a simple third-person pronoun:

• is = he
• ea = she / it
• id = it

So:

• id tangere = to touch it

Using id avoids repeating hoc vitrum.

Id is accusative neuter singular.

It is accusative because tangere is a transitive verb and needs a direct object:

• touch what?
• touch it

Since the thing being touched is vitrum, which is neuter singular, the pronoun must also be neuter singular:

• vitrum → id

Latin word order is much more flexible than English word order. The sentence is organized more by emphasis and style than by a fixed subject-verb-object pattern.

So:

• mater infantem id tangere non sinat

is perfectly normal Latin.

The important grammatical relationships are shown by the forms:

• mater nominative
• infantem accusative
• id accusative
• tangere infinitive
• sinat finite verb

That means Latin can move words around without causing as much confusion as English would.

Yes, quite possibly. Latin often leaves out words that are understood from context.

So a sentence like:

• Hoc vitrum tam fragile est ut mater infantem tangere non sinat

could still be understood as This glass is so fragile that the mother does not allow the child to touch it.

However, including id makes the object explicit and can make the sentence clearer.

Sinere means to allow, to permit, or sometimes to let.

So non sinat means:

• does not allow
• does not permit
• won't let

Depending on style, English might translate it in slightly different ways:

• The mother does not allow the child to touch it
• The mother won't let the child touch it

Infans literally means someone not speaking, and it can refer to an infant, baby, or young child, depending on context.

So infantem could be translated as:

• the infant
• the baby
• the child

The best English choice depends on the tone and context, not just the Latin form.

It breaks down like this:

• Hoc vitrum = this glass
• tam fragile est = is so fragile
• ut = that
• mater = the mother
• infantem = the child
• id tangere = to touch it
• non sinat = does not allow

So the grammar is:

• main clause: Hoc vitrum tam fragile est
• result clause: ut mater infantem id tangere non sinat

That is why the sentence means:

• This glass is so fragile that the mother does not allow the child to touch it.