In de bibliotheek mag je fluisteren, maar de kinderen beginnen toch te schreeuwen.

Dutch often puts a place, time, or other extra piece of information at the beginning of the sentence for emphasis or simply because it sounds natural.

So instead of starting with the subject, Dutch starts with the location:

• In de bibliotheek = In the library

This is called putting an element in the first position. In a main clause, the finite verb then has to come next.

That is why you get:

• In de bibliotheek mag je fluisteren
• not In de bibliotheek je mag fluisteren

Because Dutch main clauses usually follow the verb-second rule.

That means the finite verb must be the second main element in the sentence.

Compare:

• Je mag fluisteren in de bibliotheek.
• In de bibliotheek mag je fluisteren.

In the second version, In de bibliotheek takes the first position, so the verb mag must come right after it, and the subject je moves after the verb.

This is often called inversion.

Not necessarily. Je can mean:

• you = one specific person
• you in a general sense = people / one / anyone

In this sentence, it most likely has the general meaning:

• In the library, you may whisper
  = In a library, people are allowed to whisper

So it is not only addressing one person directly.

Mag is the singular form of the verb mogen.

Here it means to be allowed to or may.

So:

• je mag fluisteren = you may whisper / you are allowed to whisper

It does not mean ability.
For ability, Dutch usually uses kunnen.

Compare:

• Je mag fluisteren. = You are allowed to whisper.
• Je kunt fluisteren. = You are able to whisper.

After a modal verb such as mogen, Dutch uses the bare infinitive.

Common modal verbs are:

• kunnen = can
• mogen = may
• moeten = must
• willen = want
• zullen = will / shall

So you say:

• je mag fluisteren
• je kunt fluisteren
• je moet fluisteren

Not:

• je mag te fluisteren

Because beginnen is not a modal verb. It is a normal verb, and in Dutch it is commonly followed by te + infinitive.

So:

• beginnen te schreeuwen = to start shouting

Other similar patterns are:

• proberen te lezen = to try to read
• vergeten te bellen = to forget to call
• hopen te winnen = to hope to win

So the contrast is:

• mag fluisteren → no te
• beginnen te schreeuwen → yes te

In this sentence, toch means something like:

• still
• anyway
• nevertheless
• despite that

It shows a contrast between what is appropriate or allowed and what actually happens.

So:

• In de bibliotheek mag je fluisteren, maar de kinderen beginnen toch te schreeuwen.

means roughly:

• In the library you may whisper, but the children still / nevertheless start shouting.

It adds the idea that their shouting goes against what you would expect.

Because de kinderen is plural, and the verb must agree with it.

• het kind begint = the child begins
• de kinderen beginnen = the children begin

So:

• singular: het kind begint toch te schreeuwen
• plural: de kinderen beginnen toch te schreeuwen

Also note that kinderen is the irregular plural of kind.

The second clause is:

• maar de kinderen beginnen toch te schreeuwen

Its structure is:

• maar = but
• de kinderen = subject
• beginnen = finite verb
• toch = adverb
• te schreeuwen = infinitive phrase

So Dutch keeps the normal main-clause order here:

subject + finite verb + other elements + infinitive phrase

That is a very common beginner question.

In this sentence:

• beginnen is the finite verb
• schreeuwen is an infinitive

They happen to look similar because many Dutch verb forms end in -en.

How to tell the difference:

1. Beginnen matches the subject de kinderen, so it is the verb that is actually conjugated here.
2. Schreeuwen comes after te, which is a strong sign that it is an infinitive.
3. In a main clause, the finite verb usually comes earlier in the clause.

So:

• de kinderen beginnen = the children begin
• te schreeuwen = to shout

Maar means but and joins two main clauses.

It signals contrast:

• first clause: whispering is what is allowed
• second clause: the children do something different from what you would expect

So the sentence sets up a clear opposition:

• you may whisper
• but the children start shouting anyway

Yes. That is also correct.

Compare:

• Je mag in de bibliotheek fluisteren.
• In de bibliotheek mag je fluisteren.

Both mean the same basic thing, but the emphasis changes slightly.

• Je mag in de bibliotheek fluisteren starts with you
• In de bibliotheek mag je fluisteren starts with the location, so it highlights in the library

Dutch is quite flexible about what comes first, but the verb-second rule still applies in main clauses.

Yes.

• fluisteren = to whisper
• schreeuwen = to shout / scream / yell

Both are very common verbs.

Examples:

• Ze fluistert heel zacht. = She whispers very softly.
• De kinderen schreeuwen buiten. = The children are shouting outside.

In your sentence, the contrast between fluisteren and schreeuwen is especially strong, which helps make the sentence feel vivid.