A fogkefe a pohár mellett van, a fogkrém pedig a tükör előtt.

In Hungarian, a / az is the definite article, so it means the.

• a fogkefe = the toothbrush
• a pohár = the cup/glass
• a fogkrém = the toothpaste
• a tükör = the mirror

Hungarian indefinite a/an is egy.

So:

• egy fogkefe = a toothbrush
• a fogkefe = the toothbrush

Also, Hungarian uses a before consonant sounds and az before vowel sounds.

Hungarian often uses the definite article more regularly than English does. In this sentence, all four nouns are specific, identifiable objects, so they all take a:

• a fogkefe
• a pohár
• a fogkrém
• a tükör

This can feel repetitive to an English speaker, but it is normal Hungarian.

They are compound words:

• fog = tooth
• kefe = brush
• fogkefe = toothbrush

and

• fog = tooth
• krém = cream
• fogkrém = toothpaste

Compound nouns are very common in Hungarian.

Because Hungarian often uses postpositions instead of prepositions.

English says:

• next to the cup
• in front of the mirror

Hungarian says the noun first, then the postposition:

• a pohár mellett = next to the cup
• a tükör előtt = in front of the mirror

So:

• mellett = next to / beside
• előtt = in front of / before

This is one of the basic word-order differences between English and Hungarian.

Many Hungarian postpositions take a noun phrase in its basic form, usually with the article if needed:

• a pohár mellett
• a tükör előtt

So the relationship is shown by the postposition itself, not by adding a case ending to the noun.

English learners sometimes expect an extra ending somewhere, but here mellett and előtt already do the job.

That is a very common and important question.

In Hungarian, the verb to be is often omitted in the 3rd person singular/plural present tense when you are identifying or describing something:

• A fogkefe kicsi. = The toothbrush is small.
• Ez a fogkefe. = This is the toothbrush.

But when you express location, Hungarian normally uses van:

• A fogkefe a pohár mellett van. = The toothbrush is next to the cup.

So:

• description / identification → often no van
• location / existence → usually van

The full version could be:

• A fogkefe a pohár mellett van, a fogkrém pedig a tükör előtt van.

But Hungarian often omits repeated words when the meaning is clear. Since the second clause has the same verb, van is left out.

So the sentence is perfectly natural with only one van.

Pedig is a connecting word that often means something like:

• while
• whereas
• and as for
• sometimes simply and, but with contrast or comparison

Here it links the two items and slightly contrasts their locations:

• the toothbrush is next to the cup, while the toothpaste is in front of the mirror

So pedig is not exactly the same as plain és (and). It gives a sense of meanwhile / on the other hand / as for the other item.

Yes, you could say:

• A fogkefe a pohár mellett van, és a fogkrém a tükör előtt van.

That is grammatical, but it sounds more neutral and a bit less elegant in this kind of paired statement.

Using pedig is more natural when you are setting two things side by side:

• the toothbrush ...
• the toothpaste, meanwhile / on the other hand ...

So pedig is a very good choice here.

Hungarian word order is flexible, but it is strongly shaped by topic and focus.

In this sentence:

• A fogkefe is the topic: what we are talking about
• a pohár mellett van says where it is

So the structure is very natural:

• [topic] + [location] + van

The second clause works the same way:

• a fogkrém = topic
• a tükör előtt = location

You could change the word order in some contexts, but that would change the emphasis.

Yes. Előtt can express either:

1. space: in front of
2. time: before

Examples:

• A tükör előtt van. = It is in front of the mirror.
• Hat óra előtt. = Before six o’clock.

Here, because we are talking about physical objects and location, it clearly means in front of.

Pohár often means glass in the everyday sense of a drinking glass, but depending on context it may be translated more generally as cup or drinking vessel.

So a pohár mellett could be understood as:

• next to the glass
• sometimes next to the cup, depending on the intended meaning shown to the learner

If you already have the translation from your material, follow that meaning for this sentence.

A rough guide is:

• A fogkefe a pohár mellett van
  → aw FOG-keh-feh aw PO-haar MEH-lett vawn

• a fogkrém pedig a tükör előtt
  → aw FOG-kraim PEH-dig aw TÜ-kör EH-lött

A few helpful notes:

• gy sounds like the dy in duke for many English speakers
• ö / ő / ü / ű are rounded front vowels that English does not really have
• stress is always on the first syllable in Hungarian words:
  • FOGkefe
  • POhár
  • MELlett
  • FOGkrém
  • PEdig
  • TÜkör
  • Előtt

Only partly. A very literal version would be something like:

• The toothbrush the cup next-to is, the toothpaste meanwhile the mirror in-front-of.

That sounds unnatural in English because Hungarian and English organize location differently:

• Hungarian uses postpositions
• English uses prepositions
• Hungarian allows the second van to be omitted

So it is better to understand the structure rather than translate each word mechanically.