No pueden despedir a la empleada.

Because pueden is a conjugated modal verb from poder (to be able to / can), and despedir stays in the infinitive.

This is the normal pattern in Spanish:

• pueden despedir = they can fire
• quieren despedir = they want to fire
• van a despedir = they are going to fire

So pueden carries the tense and subject, while despedir gives the main action.

No makes the sentence negative.

• Pueden despedir a la empleada. = They can fire the employee.
• No pueden despedir a la empleada. = They cannot / can’t fire the employee.

In Spanish, no usually goes directly before the conjugated verb, which here is pueden.

This is the personal a.

In Spanish, when the direct object is a specific person, you usually put a before it.

So:

• despedir a la empleada = fire the employee
• veo a María = I see María
• conocen al profesor = they know the teacher

Even though la empleada is the direct object, Spanish still uses a because it refers to a person.

Because la and a are doing different jobs.

• la empleada = the employee
• a = marks that this person is the direct object

So in despedir a la empleada, the full object is a la empleada.

This does not mean to the employee here. The a is grammatical, not a literal English to.

Because pueden is the third-person plural form of poder, and in Spanish that form can mean:

• they can
• you all can

The exact meaning depends on context.

So this sentence could mean:

• They can’t fire the employee
• You all can’t fire the employee

In many learning contexts, they can’t fire the employee is the default reading unless the situation suggests otherwise.

It is not stated explicitly. Spanish often omits subject pronouns when the verb already shows who the subject is.

So instead of saying:

• Ellos no pueden despedir a la empleada

Spanish often just says:

• No pueden despedir a la empleada

This is very normal. The verb pueden already tells you the subject is they or you all.

Because empleada is the feminine form, meaning a female employee.

• el empleado = the male employee / employee in masculine form
• la empleada = the female employee

The article changes too:

• el with masculine singular nouns
• la with feminine singular nouns

So this sentence specifically refers to a woman.

Here, despedir means to fire, to dismiss, or to let go from a job.

But be careful: despedir can have other meanings in other contexts, such as to say goodbye to or to see someone off.

Examples:

• Despidieron al empleado. = They fired the employee.
• Fueron a despedir a Ana al aeropuerto. = They went to see Ana off at the airport.

In your sentence, because the object is la empleada and the meaning is already about work, it clearly means fire.

Yes. That is very natural.

• No pueden despedir a la empleada.
• No pueden despedirla.

Here la replaces a la empleada because she is the direct object.

Notice that when you use the object pronoun, the personal a disappears:

• a la empleada → la

Both versions are correct. The full noun phrase is clearer; the pronoun version is more concise.

With an infinitive like despedir, object pronouns can often go in two places:

• before the conjugated verb: No la pueden despedir
• attached to the infinitive: No pueden despedirla

Both are correct and common.

So you can say:

• No pueden despedir a la empleada.
• No la pueden despedir.
• No pueden despedirla.

All mean the same thing.

Yes. Pueden is the present tense of poder.

So the sentence literally uses the present:

• No pueden despedir a la empleada.

Depending on context, English might translate it as:

• They can’t fire the employee
• They are not allowed to fire the employee

Spanish present tense often covers ideas that English expresses in slightly different ways.

It can mean either one. Context decides.

• inability: They are unable to fire the employee.
• lack of permission / legal possibility: They are not allowed to fire the employee.
• practical impossibility: They can’t fire the employee because of the situation.

Spanish poder covers both ability and possibility/permission, just like can in English often does.

In standard Spanish, yes, that would sound wrong because la empleada is a specific person and needs the personal a.

So the correct version is:

• No pueden despedir a la empleada.

The a is an important part of the sentence structure here.

Yes, that is grammatically correct.

But Spanish often leaves out ellos unless you want to:

• add emphasis
• create contrast
• avoid ambiguity

For example:

• Ellos no pueden despedir a la empleada, pero nosotros sí.

Without special emphasis, the shorter version is usually more natural:

• No pueden despedir a la empleada.

You could make it less specific by changing the object.

For example:

• No pueden despedir a una empleada. = They can’t fire an employee.
• No pueden despedir empleados. = They can’t fire employees.
• No pueden despedir al personal. = They can’t fire the staff.

Your original sentence, No pueden despedir a la empleada, refers to a specific female employee.