A memóriakártya annyira tele van, hogy nem tudok több fotót készíteni.

It means so ... that.

So:

• annyira tele van = is so full
• hogy nem tudok több fotót készíteni = that I can’t take any more photos

This is a very common Hungarian pattern for showing degree + result:

• annyira fáradt vagyok, hogy elalszom = I’m so tired that I’m falling asleep
• annyira hideg van, hogy... = it’s so cold that...

Annyira is an adverb of degree. It modifies tele and means so, to such an extent, or that much.

So annyira tele van is literally something like is full to such an extent.

Without annyira, the sentence would lose the so ... that structure. You could still say A memóriakártya tele van, but then you would normally need a different way to express the consequence, such as ezért = therefore / so.

Because tele van is the normal Hungarian expression for is full.

Hungarian often leaves out van in 3rd person present with adjectives, but tele is commonly used in the fixed pattern tele van. So:

• A memóriakártya tele van = The memory card is full

That is the natural form.

If you say only tele, it sounds incomplete in this kind of sentence.

Also, when you want to say what something is full of, Hungarian often uses:

• tele van valamivel = is full of something

For example:

• A kártya tele van fotókkal = The card is full of photos

Here hogy introduces the result clause and means that.

So the structure is:

• annyira ... hogy ... = so ... that ...

In English, that is sometimes optional, but in Hungarian hogy is normally expressed in this pattern.

Here it means I can’t.

The verb tud can mean both:

• to know
• to be able to / can

The context tells you which meaning is intended.

In this sentence, the problem is that the memory card is full, so nem tudok több fotót készíteni clearly means:

• I can’t take any more photos

not

• I don’t know how to take more photos

Because the object is indefinite: több fotót = more photos.

Hungarian has two conjugations:

• indefinite
• definite

Here the verb is tudok because the thing being done, több fotót készíteni, involves an indefinite object.

Compare:

• Nem tudok több fotót készíteni. = I can’t take more photos.
• Nem tudom elkészíteni a fotókat. = I can’t take/make the photos.

In the second sentence, a fotókat is definite, so tudom is used.

Because after numbers and quantity words, Hungarian normally uses the singular noun, not the plural.

This is very important for English speakers.

So Hungarian says:

• két könyv = two books
• sok ember = many people
• több fotó = more photos

Then, because fotó is the direct object here, it gets the accusative ending:

• több fotót

So:

• több fotót készíteni = to take more photos

not több fotókat.

Because it is the direct object of készíteni.

Hungarian marks direct objects with the accusative ending -t.

So:

• fotó = photo
• fotót = photo as a direct object

In this sentence, the thing you cannot take/make is more photos, so Hungarian marks fotó with -t:

• több fotót készíteni

Yes, készíteni literally means to make / to produce, but it is a normal Hungarian way to talk about taking photos.

So:

• fotót készíteni = to take a photo
• literally: to make a photo

This is just a difference in idiom between the two languages.

You may also hear:

• fotózni = to photograph / to take photos
• képet készíteni = to make/take a picture

All of these are natural, though the exact style can vary a little.

Yes. Hungarian very often writes compounds as one word, especially noun + noun combinations.

So:

• memória = memory
• kártya = card
• memóriakártya = memory card

This is completely normal in Hungarian spelling.

A is the definite article, meaning the.

So:

• A memóriakártya = the memory card

It is used because the sentence is talking about a specific memory card, not just any memory card.

Also remember:

• a is used before consonant sounds
• az is used before vowel sounds

Since memóriakártya begins with m, the correct form is a.

Yes, Hungarian word order is flexible, but changing it usually changes the focus or emphasis.

The original sentence is neutral and natural:

• A memóriakártya annyira tele van, hogy nem tudok több fotót készíteni.

You could also say:

• Annyira tele van a memóriakártya, hogy nem tudok több fotót készíteni.

This puts more emphasis on how full the card is.

You could also emphasize the object:

• ... hogy több fotót nem tudok készíteni.

That highlights more photos.

So yes, the order can change, but the original version is a very normal, straightforward way to say it.