Chủ thẻ đang tìm thẻ ghi nợ.

Chủ thẻ means cardholder.

Literally:

• chủ = owner, person in charge
• thẻ = card

So chủ thẻ is the person who owns or holds the card. In banking and payment contexts, cardholder is the most natural English translation.

Because the two instances of thẻ are doing different jobs:

• chủ thẻ = cardholder
• thẻ ghi nợ = debit card

So the first thẻ is part of the subject, and the second thẻ is the object being looked for.

This repetition may look strange in English, but it is completely normal in Vietnamese.

Đang marks an action as being in progress.

So:

• tìm = look for, search
• đang tìm = is looking for, is searching for

It works a lot like the English progressive form is looking.

Yes.

Chủ thẻ tìm thẻ ghi nợ is still grammatical, but it is less explicit about the action happening right now. Without đang, the sentence can sound more neutral and can depend more on context.

With đang, the listener clearly understands that the searching is currently in progress.

Usually tìm means look for / search for.

That is why đang tìm is best understood as is looking for.

If you want to express the idea of actually finding something, Vietnamese often uses tìm thấy:

• tìm = look for
• tìm thấy = find, succeed in finding

So this sentence does not mean that the cardholder has already found the debit card.

Because Vietnamese noun modifiers usually come after the noun.

Here:

• thẻ = card
• ghi nợ = debit

So thẻ ghi nợ literally follows the Vietnamese pattern card debit, but in natural English we say debit card.

This same pattern appears in many similar expressions:

• thẻ tín dụng = credit card
• tài khoản ngân hàng = bank account

Literally, ghi nợ has the idea of recording a debt/debit. In banking Vietnamese, it functions as the standard term for debit.

So thẻ ghi nợ is the normal way to say debit card.

You do not need to analyze it every time word by word; it is best learned as a set phrase.

Vietnamese does not have articles like English a/an/the.

So chủ thẻ could mean:

• the cardholder
• a cardholder

And thẻ ghi nợ could mean:

• the debit card
• a debit card

The exact meaning depends on context. In many learning examples, English translations choose the or a based on what sounds most natural in the situation.

Not in this sentence.

Vietnamese does not require a classifier every time a noun appears. Here, thẻ ghi nợ can stand by itself as the object.

If you add a number or make it more specific, you may see forms like:

• một thẻ ghi nợ = a debit card
• một chiếc thẻ ghi nợ = a debit card

So a classifier is possible in some contexts, but it is not necessary here.

No. Chủ thẻ is gender-neutral.

It can refer to a male or female cardholder. Vietnamese nouns like this usually do not show gender by themselves. If gender matters, it is normally shown somewhere else in the sentence or in the wider context.