A könyvtáros azt javasolja, hogy jegyezzem elő a példányt.

A natural breakdown is:

• A könyvtáros = the librarian
• azt = that / it
  This points forward to the whole clause that follows.
• javasolja = suggests / recommends
• hogy = that
• jegyezzem elő = that I reserve / place on hold
• a példányt = the copy / the item

So the structure is basically:

• The librarian suggests that I reserve the copy.

Hungarian often builds this as:

• [subject] + azt + [verb] + hogy-clause

This azt is very common in Hungarian before a hogy-clause.

It works like a forward-pointing object:

• azt javasolja, hogy... = suggests that...

So azt refers to the whole following clause:

• azt = that thing / the following idea
• hogy jegyezzem elő a példányt = the content of that idea

In English, we usually do not translate azt separately here, but in Hungarian it sounds very natural.

Because Hungarian is using the definite conjugation here.

The verb javasol means to suggest / recommend.
In this sentence, its object is azt, which is definite, so the verb takes a definite form:

• javasol = indefinite
• javasolja = definite, he/she suggests it / that

So:

• A könyvtáros javasolja... would sound incomplete unless something definite is understood
• A könyvtáros azt javasolja, hogy... is the standard full pattern

hogy introduces a subordinate clause, usually equivalent to that in English.

So:

• azt javasolja = suggests that
• hogy jegyezzem elő a példányt = that I reserve the copy

Hungarian uses hogy very often in this kind of sentence.
English sometimes drops that, but Hungarian usually keeps hogy.

Because this is a subjunctive / imperative-type form in the definite conjugation.

After verbs like javasol meaning suggest, Hungarian normally uses:

• hogy + subjunctive-type verb form

Here the verb is part of előjegyez = to reserve / place on hold.

The object is a példányt, which is definite, so the verb must also be definite:

• jegyezzek = I should write/register something indefinite
• jegyezzem = I should write/register it / the definite object

So jegyezzem elő a példányt means that I reserve the copy.

Because előjegyez is a prefixed verb, and in this kind of subjunctive / imperative construction, the prefix often moves after the finite verb.

So the dictionary form is:

• előjegyez = to reserve

But in this sentence:

• jegyezzem elő

This is completely normal Hungarian.

Compare the same pattern with other verbs:

• elolvas = to read through

• olvassam el = that I read it through

• megvesz = to buy
• vegyem meg = that I buy it

So jegyezzem elő is the expected form here.

In a library context, előjegyez means something like:

• to reserve
• to place on hold
• to request in advance

So this is not just the literal combination of elő + jegyez.
As a whole, it is a set expression used for reserving a library item.

That is why jegyezzem elő a példányt is best understood as:

• that I place a hold on the copy
• that I reserve the copy

The -t marks the accusative, which is the direct object case.

So:

• példány = copy / экземпляр-like physical item
• példányt = the copy as the object of the verb

In library language, példány usually means a specific physical copy of a book or other item, not just the title in general.

So:

• a példányt = the copy / the item

Yes, Hungarian word order is flexible, but the version you have is the neutral, natural one.

Current structure:

• A könyvtáros = topic
• azt javasolja = main verb phrase
• hogy jegyezzem elő a példányt = subordinate clause

Inside the subordinate clause, jegyezzem elő a példányt is also neutral.

If you changed the order, you would usually add emphasis or contrast. For example:

• A könyvtáros azt javasolja, hogy a példányt jegyezzem elő.

This would put more attention on the copy.

So yes, word order can change, but the original sentence is the ordinary, unmarked version.

The hardest parts for English speakers are usually könyvtáros and jegyezzem.

A rough guide:

• könyvtáros ≈ könyv-taa-rosh
• jegyezzem ≈ ye-dyezz-em

A few important sound notes:

• ö has no exact English equivalent; it is like German ö
• ny sounds like the ny in canyon
• j sounds like English y
• gy is a soft consonant, roughly like dy
• s in Hungarian sounds like English sh
• á is a long vowel, like the a in father

So:

• könyvtáros has sh at the end, not s
• javasolja is roughly yo-vo-shol-yo
• példányt contains ny again

If you want, a more learner-friendly pronunciation target for the whole sentence is:

• A könyvtáros azt javasolja, hogy jegyezzem elő a példányt
• aw könyv-taa-rosh awst yo-vo-shol-yo, hodj ye-dyezz-em uh-lö a payl-daanyt

That is only approximate, but it is a useful starting point.