A könyvtárban nem beszélhetsz hangosan.

A is the Hungarian definite article, so here it means the.

• a könyvtár = the library
• egy könyvtár = a library

Hungarian has two forms of the definite article:

• a before a consonant
• az before a vowel

Since könyvtár starts with k, it takes a.

It is made of:

• könyvtár = library
• -ban = in

So könyvtárban means in the library.

Hungarian very often uses case endings like -ban/-ben instead of separate words such as in.

Because of vowel harmony.

Hungarian suffixes often have different forms depending on the vowels in the word. The pair -ban / -ben both mean in, but:

• -ban usually goes with words containing back vowels
• -ben usually goes with words containing front vowels

könyvtár takes -ban, so:

• könyvtárban = in the library

This is something you mostly get used to with exposure, though vowel harmony rules help a lot.

It breaks down like this:

• beszél = speak
• -het = can / may
• -sz = you (singular, informal)

So:

• beszélhetsz = you can speak / you may speak

With nem in front:

• nem beszélhetsz = you cannot / may not speak

Again, this is vowel harmony.

The modal suffix is:

• -hat
• -het

Since beszél has front vowels, it takes -het:

• beszélhet = can speak
• beszélhetsz = you can speak

It can mean either, depending on context.

Grammatically, nem beszélhetsz means something like:

• you cannot speak
• you may not speak

In this sentence, because it is about a library rule, the natural meaning is:

• you mustn’t speak loudly
• you’re not allowed to speak loudly

So here it is more about permission/prohibition than physical ability.

Because Hungarian verbs usually already show the subject.

The ending -sz in beszélhetsz tells you the subject is:

• you (singular, informal)

So Hungarian often leaves out pronouns when they are not needed.

You could add te for emphasis:

• Te nem beszélhetsz hangosan.

That would sound more like You may not speak loudly.

• hangos = loud (adjective)
• hangosan = loudly (adverb)

Here the word describes how someone speaks, so Hungarian uses the adverb:

• hangosan beszélni = to speak loudly

So:

• hangos ember = a loud person
• hangosan beszél = speaks loudly

Because the meanings are different.

• nem beszélsz hangosan = you do not speak loudly
  • this sounds like a fact, habit, or description
• nem beszélhetsz hangosan = you may not / must not speak loudly
  • this expresses permission or a rule

So the -het part is important: it changes the sentence from a simple statement into something about what is allowed.

Yes. Hungarian word order is flexible, and changing it often changes emphasis rather than basic meaning.

For example:

• A könyvtárban nem beszélhetsz hangosan.

  • In the library, you may not speak loudly.
  • The place is the topic.

• Nem beszélhetsz hangosan a könyvtárban.

  • You may not speak loudly in the library.
  • Very natural too.

If you move hangosan earlier, it can sound more contrastive, as if you mean:

• loudly, no — but perhaps quietly, yes

So the original order is natural and neutral for stating a rule about the library.

A few useful points:

• sz is pronounced like English s
• s is pronounced like English sh
• ny is like Spanish ñ, or the ny sound in canyon
• ö is a rounded front vowel; English does not have an exact match

So:

• könyvtárban is roughly könyv-tár-ban
• beszélhetsz has sz at the end, so it ends with an s sound, not z

Also, Hungarian stress is usually on the first syllable of each word.

Yes. beszélhetsz is second person singular informal, so it is used with te.

Other versions would be:

• A könyvtárban nem beszélhet hangosan.

  • formal singular: You may not speak loudly in the library.

• A könyvtárban nem beszélhettek hangosan.

  • informal plural: You all may not speak loudly in the library.

• A könyvtárban nem beszélhetnek hangosan.

  • formal plural, or they may not speak loudly, depending on context

So the ending changes depending on who you are talking to.