Compta les cartes.

Yes. Compta is also the 3rd person singular present form of comptar:

• ell compta = he counts
• ella compta = she counts

So Compta les cartes could theoretically mean He/she counts the cards if the context makes that clear. But on its own, with no subject stated, it is very commonly understood as a command: Count the cards.

Catalan often leaves subject pronouns out because the verb ending already gives enough information. This is called being a pro-drop language.

So instead of saying Tu compta les cartes, Catalan normally just says:

Compta les cartes.

Adding tu is possible, but it usually adds emphasis, contrast, or a special tone.

Because carta is a feminine noun, and cartes is plural.

So the article changes like this:

• la carta = the card
• les cartes = the cards

That is why the sentence uses les, the feminine plural definite article.

Les cartes refers to a specific set of cards, so the definite article is the normal choice.

In other words, this sounds like:

• Count the cards
• Count these/the cards

Catalan often uses an article where English also would, and in this sentence les helps show that we mean a known group of cards, not just cards in general.

A rough pronunciation for many learners is:

KOM-tuh luhs KAR-tuhs

A few helpful points:

• compta begins with a clear kom-
• the mp is pronounced
• in many accents, the final a in compta is a weak uh sound
• cartes has a tapped Catalan r, not a strong English r

Pronunciation varies by dialect, but that rough version is a good start.

The form changes depending on who you are addressing:

• Compta les cartes. = informal singular (tu)
• Compti les cartes. = formal singular (vostè)
• Compteu les cartes. = informal plural (vosaltres)
• Comptin les cartes. = formal plural (vostès)

So the sentence you were given is specifically the informal singular command.

Yes. The direct-object pronoun for les cartes is les.

With an affirmative command, the pronoun is attached to the end of the verb:

Compta-les. = Count them.

This is a very common pattern in Catalan. If you later learn negative commands, the pronoun usually moves before the verb:

No les comptis. = Don't count them.