A tepsi a tűzhely mellett van.

Because Hungarian uses the definite article a / az much like English the.

• a tepsi = the baking tray
• a tűzhely = the stove

So the sentence literally looks like:

• The baking tray the stove next to is

Hungarian often uses the definite article in places where English also uses the, so having it twice is completely normal.

Tepsi usually means baking tray, oven tray, or sometimes baking pan, depending on context.

It refers to a flat or shallow tray used for baking. In everyday translation, baking tray or oven tray is often the best choice.

Tűzhely means stove, cooker, or sometimes range, depending on the variety of English.

It is the appliance used for cooking. In many learning materials, stove is the simplest translation.

Mellett means next to or beside.

In this sentence:

• a tűzhely mellett = next to the stove

So mellett is the word that expresses location relative to something else.

Because mellett is a postposition.

A postposition works a bit like an English preposition, but it comes after the noun instead of before it.

Compare:

• English: next to the stove
• Hungarian: the stove next to → a tűzhely mellett

So tűzhely stays in its basic form, and mellett comes after it.

Van is the 3rd person singular form of lenni, meaning to be.

Here it means is:

• A tepsi a tűzhely mellett van.
• The baking tray is next to the stove.

That is a very common and important question.

In Hungarian, van is often omitted in the present tense when the predicate is a noun or adjective:

• A tepsi nagy. = The tray is big.
• A tepsi fém. = The tray is metal.

But when the sentence expresses location, existence, or similar ideas, van is normally used:

• A tepsi az asztalon van. = The tray is on the table.
• A tepsi a tűzhely mellett van. = The tray is next to the stove.

So in this sentence, van is needed because we are talking about where something is.

This is a very natural neutral Hungarian word order:

• A tepsi = topic / what we are talking about
• a tűzhely mellett = location
• van = verb

So the structure is basically:

• [thing] [where it is] [is]

Hungarian word order is flexible, but this version sounds like a straightforward statement.

Yes. Hungarian word order is flexible, and different orders can change the emphasis.

For example:

• A tűzhely mellett van a tepsi.

This still means roughly The baking tray is next to the stove, but it may sound more like you are focusing on where it is, or answering a question like Where is the baking tray?

So the original sentence is neutral, while other word orders can shift emphasis.

A rough pronunciation guide:

• tűzhely ≈ tyoozh-hay, but not exactly

A few details:

• tű contains ű, a long rounded vowel that English does not really have
• zs is pronounced like the s in measure
• hely sounds roughly like hey, though the ly spelling is historical in modern Hungarian

So tűzhely is approximately tyoozh-hey, but with a specifically Hungarian vowel in the first syllable.

Tepsi is roughly:

• TEP-shee

More exactly:

• tep as in step without the s
• si sounds like shee

Stress in Hungarian is always on the first syllable, so:

• TEP-si

Hungarian has two forms of the definite article:

• a
• az

The choice depends on the following sound:

• a before a consonant
• az before a vowel

So here:

• a tepsi
• a tűzhely

because both following words begin with consonants.

Compare:

• az asztal = the table

The basic form is mellett.

It is one member of a small set of related location words. For example:

• mellett = next to / beside (location)
• mellé = to next to / to the side of (movement toward)
• mellől = from next to (movement away)

Examples:

• A tepsi a tűzhely mellett van. = The tray is next to the stove.
• A tepsit a tűzhely mellé teszem. = I put the tray next to the stove.
• Elveszem a tepsit a tűzhely mellől. = I take the tray away from beside the stove.

This location / motion distinction is very important in Hungarian.

In standard Hungarian, you would normally say:

• A tepsi a tűzhely mellett van.

Leaving out the article before tűzhely would usually sound unnatural here, unless there were some very special context.

So if you mean next to the stove, keep the article:

• a tűzhely mellett

A very literal breakdown is:

• A tepsi = the baking tray
• a tűzhely mellett = next to the stove / literally the stove beside
• van = is

So word-for-word, it is something like:

• The baking tray the stove beside is.

That sounds wrong in English, of course, but it helps show how Hungarian is built.