A fényképezőgép a táskában van.

Because a/az is the Hungarian definite article, meaning the.

So:

• a fényképezőgép = the camera
• a táskában = in the bag

Hungarian, like English, uses the article separately with each definite noun phrase. So having two a words here is completely normal.

Hungarian has two forms of the definite article:

• a before consonant sounds
• az before vowel sounds

Since fényképezőgép and táskában both begin with consonant sounds, the correct article is a.

For example:

• a táska = the bag
• az autó = the car

The ending -ban/-ben means in or inside.

So:

• táska = bag
• táskában = in the bag

Hungarian often expresses meanings like in, on, to, from, and so on with suffixes attached directly to the noun, instead of separate prepositions as in English.

So English in the bag becomes Hungarian a táskában.

Because the final a in táska becomes long á before many suffixes.

So:

• táska → táskában
• not táskaban

This is a very common pattern in Hungarian:

• szoba → szobában
• iskola → iskolában

The same thing happens with final e, which often becomes é before suffixes.

This is because of vowel harmony, one of the most important patterns in Hungarian.

Hungarian suffixes often have different forms depending on the vowels in the word. Very roughly:

• words with back vowels usually take -ban
• words with front vowels usually take -ben

táska contains back vowels, so it takes -ban:

• táskában

Compare:

• házban = in the house
• székben = in the chair
• kertben = in the garden

That is a very common and very good question.

Hungarian often omits van in the present tense, third person, but not in every kind of sentence.

For example, with simple identity or description:

• A fényképezőgép új. = The camera is new.
• Péter tanár. = Peter is a teacher.

Here van is omitted.

But in location sentences, Hungarian normally keeps van:

• A fényképezőgép a táskában van. = The camera is in the bag.

So in this sentence, van is needed.

Yes, you could. Both are correct, but they put the focus in different places.

• A fényképezőgép a táskában van.
  This starts with the camera as the topic, then says where it is.

• A táskában van a fényképezőgép.
  This starts with in the bag, and sounds more like an answer to What is in the bag?

Hungarian word order is more flexible than English word order. It often reflects topic, focus, and emphasis, not just grammar.

This is the difference between location and movement toward.

• táskában = in the bag
  This describes where something is.

• táskába = into the bag
  This describes movement into the bag.

So:

• A fényképezőgép a táskában van. = The camera is in the bag.
• A fényképezőgépet a táskába teszem. = I put the camera into the bag.

This is a very important contrast in Hungarian.

Because Hungarian very often forms words by combining smaller meaningful parts into one compound word.

fényképezőgép basically means something like photo-taking machine.

You can think of it roughly like this:

• fénykép = photograph
• fényképez = to photograph
• gép = machine/device

So fényképezőgép is the ordinary Hungarian word for camera.

Long compound nouns are very normal in Hungarian.

A helpful breakdown is:

• fény-ké-pe-ző-gép

A few useful points:

• The stress is on the first syllable: FÉNYképezőgép
• é is a long vowel
• ő is also a long vowel
• ny is a single consonant sound, similar to the ny in canyon for many English speakers

You do not need perfect pronunciation right away, but it helps to read it as a sequence of clear syllables rather than trying to guess it from English spelling rules.