Tegnap használtam utoljára a bankkártyát.

Because Hungarian usually drops subject pronouns when the verb already shows who is doing the action.

Here, használtam already means I used:

• használ- = use
• -t- = past tense
• -am = I

So én is unnecessary unless you want extra emphasis:

• Én használtam utoljára a bankkártyát. = I was the one who used the bank card last.

Használtam breaks down like this:

• használ- = the verb stem, use
• -t- = past tense marker
• -am = first person singular ending

So használtam = I used.

Hungarian past tense is usually expressed in one word, not with an auxiliary like English did or have.

Yes, this is a sentence with a definite object: a bankkártyát = the bank card.

But there is an important detail: in the past tense, first person singular, the definite and indefinite forms are often the same.

So:

• használtam egy kártyát = I used a card
• használtam a kártyát = I used the card

Both use használtam.

You can see the difference more clearly in other persons. For example:

• használtál egy kártyát = you used a card
• használtad a kártyát = you used the card

Because bankkártya is the direct object of the verb használ (to use), so it takes the accusative ending.

• bankkártya = bank card
• bankkártyát = bank card + -t accusative ending

Also notice that the final a becomes long á before this ending:

• bankkártya → bankkártyát

That vowel lengthening is very common in Hungarian.

A is the Hungarian definite article, meaning the.

So:

• a bankkártyát = the bank card

It shows that we are talking about a specific card, not just any bank card.

Without the article, the sentence would sound different and less natural in this context.

Here utoljára means for the last time.

So the sentence is not just about a past use of the card. It says that yesterday was the last occasion on which I used it.

This is an adverb, and Hungarian often uses a single adverb where English uses a longer phrase:

• utoljára = for the last time

This is a very useful distinction.

• utoljára = for the last time, often with a sense of finality
• legutóbb = most recently / last time

So:

• Tegnap használtam utoljára a bankkártyát.
  = Yesterday was the final time I used the bank card.
• Legutóbb tegnap használtam a bankkártyát.
  = The most recent time I used the bank card was yesterday.

English last can mean either of these, but Hungarian often separates the two ideas more clearly.

Because Hungarian word order is flexible, and the first part of the sentence often sets the scene or highlights what the speaker wants to foreground.

Starting with tegnap puts attention on the time:

• Tegnap használtam utoljára a bankkártyát.

That can feel like:

• Yesterday was the day I last used the bank card.

So the beginning of the sentence is often about emphasis or information structure, not just fixed grammar rules.

Yes, often you can, but the emphasis changes.

For example:

• Tegnap használtam utoljára a bankkártyát.
  Focuses naturally on yesterday.
• A bankkártyát tegnap használtam utoljára.
  Brings the bank card to the front.
• Utoljára tegnap használtam a bankkártyát.
  Highlights the last-time/yesterday connection.

The core meaning stays similar, but the sentence may sound more natural in one context than another depending on what you want to stress.

Because Hungarian normally writes many noun compounds as one word.

• bank = bank
• kártya = card
• bankkártya = bank card

This is very normal in Hungarian spelling. English is looser about compounds, but Hungarian usually joins them into a single word.

Not necessarily.

Bankkártya usually means a bank card in a general sense, often something like a debit card or ATM/bank-issued card.

If you specifically mean credit card, Hungarian often uses:

• hitelkártya = credit card

So bankkártya is a broader, less specific word.