Quieren impugnar el acuerdo.

Quieren is the 3rd person plural present indicative form of querer.

So it can mean:

• they want
• you all want if the subject is ustedes

In this sentence, without more context, quieren could refer to ellos, ellas, or ustedes.

Spanish often leaves out subject pronouns because the verb ending already gives that information.

So instead of saying:

• Ellos quieren impugnar el acuerdo

Spanish very naturally says:

• Quieren impugnar el acuerdo

This is completely normal. The subject is understood from context.

Because after querer, Spanish normally uses:

• querer + infinitive

So:

• quieren impugnar = they want to challenge / contest

You do not say quieren impugnan.

This is the same pattern as:

• quiero comer = I want to eat
• quieren salir = they want to leave

Here it means want.

With an infinitive, querer usually means to want to do something:

• quieren impugnar = they want to challenge

Querer can also mean to love or to care for, but that is usually clearer in other contexts, often with a noun or person:

• Quiere a su abuela = He/She loves his/her grandmother

So in this sentence, want is the correct idea.

Impugnar is a fairly formal word. It often appears in legal, administrative, political, or official contexts.

It means something like:

• to challenge
• to contest
• to dispute formally
• sometimes to appeal against, depending on context

So this is not the most casual everyday verb. It suggests a formal objection to the validity or legality of the agreement.

Not especially in casual conversation. It sounds formal and often legal/official.

In everyday speech, people might more often use verbs like:

• cuestionar = to question
• discutir = to argue about
• oponerse a = to oppose

But impugnar is the right word when someone is formally contesting a decision, agreement, result, or ruling.

El acuerdo usually means:

• the agreement
• sometimes the decision
• sometimes the settlement or resolution, depending on context

It refers to a specific agreement already known in the conversation or text.

So el acuerdo is not just any agreement, but the agreement in question.

Because el means the, so the speaker is talking about a specific agreement.

• el acuerdo = the agreement
• un acuerdo = an agreement

Using el suggests that both speaker and listener already know which agreement is being discussed.

Because el acuerdo is the direct object of impugnar, and it is a thing, not a person.

Spanish only uses the personal a with specific people (and sometimes pets or personified beings), for example:

• Veo a María = I see María

But here:

• impugnar el acuerdo

is just verb + direct object, with no a needed.

Yes, grammatically it could, because quieren can also be the form used with ustedes.

However, since this is Spanish from Spain, there is an important detail:

• In Spain, ustedes quieren is usually formal
• For informal you all, Spain normally uses vosotros queréis

So in Spain:

• Quieren impugnar el acuerdo could mean They want to challenge the agreement
• or You all want to challenge the agreement, but only in a formal sense

It is in the present indicative.

• quieren = present tense of querer
• impugnar = infinitive

So the sentence literally means something like:

• They want to challenge the agreement

Depending on context, present tense in Spanish can sometimes also sound natural in English as:

• They are looking to challenge the agreement
• They intend to challenge the agreement

But the basic tense is still present.

Yes, they are related, but they are used differently.

• acuerdo as a noun means agreement
• acordarse is a verb meaning to remember

Examples:

• el acuerdo = the agreement
• me acuerdo = I remember

So although they share the same root, in this sentence acuerdo is clearly a noun, not part of the verb acordarse.

You could say:

• Ellos quieren impugnar el acuerdo = They want to challenge the agreement
• Ellas quieren impugnar el acuerdo = They want to challenge the agreement
• Ustedes quieren impugnar el acuerdo = You all want to challenge the agreement (formal, in Spain)

And for informal plural you in Spain, you would use:

• Vosotros queréis impugnar el acuerdo
• Vosotras queréis impugnar el acuerdo

So the original sentence leaves the subject open, but the verb form narrows it down to a plural subject.