El médico ya no tenía ninguna hora disponible, así que tuvimos que aplazar la cita.

Ya no means no longer or not anymore. It shows a change: something was true before, but it is not true now.

So El médico ya no tenía ninguna hora disponible means that at that point, the doctor did not have any available appointment slots left.

A useful contrast:

• ya = already
• ya no = not anymore / no longer

For example:

• Ya está aquí = He’s already here.
• Ya no está aquí = He’s not here anymore.

Tenía is the imperfect past, and it is used here to describe a situation or background state in the past: the doctor had no available slots.

Spanish often uses the imperfect for:

• descriptions
• ongoing situations
• background information

Here, the lack of availability is the background situation that leads to the next action: tuvimos que aplazar la cita.

If you used tuvo, it would sound more like a completed, punctual event, which is less natural here.

Yes, it is a kind of double negative, but that is completely normal in Spanish. Spanish uses negative concord, which means several negative words can appear together in the same sentence.

So:

• no tenía ninguna hora disponible = literally something like didn’t have no available slot, but the real meaning is simply didn’t have any available slot

This is standard Spanish, not bad grammar.

More examples:

• No tengo nada = I don’t have anything.
• No vino nadie = Nobody came.

Because hora is a feminine noun, and ninguno/ninguna must agree with the noun.

• ningún
  • masculine singular noun
    
    • ningún problema
• ninguna
  • feminine singular noun
    
    • ninguna hora

So:

• ninguna hora disponible is correct
• ningún hora is incorrect

Here hora does not mean a literal sixty-minute hour in a strict sense. In medical and administrative contexts, hora often means an appointment time, time slot, or opening.

So ninguna hora disponible means:

• no available appointment slot
• no free time left for appointments

In Spain, this is a very natural way to talk about booking with a doctor, hairdresser, office, etc.

Usually, el médico suggests a male doctor, because el is masculine. If the doctor is female, standard modern Spanish in Spain would normally use la médica.

However, sometimes profession nouns can be used in a more generic way when the person’s sex is unknown or not important. Still, in this sentence, most learners would naturally read el médico as the male doctor.

Related forms:

• el médico = the male doctor
• la médica = the female doctor
• el doctor / la doctora are also common

Así que means so, therefore, or so then. It connects a cause with a result.

In this sentence:

• cause: El médico ya no tenía ninguna hora disponible
• result: tuvimos que aplazar la cita

So the structure is:

• X, así que Y = X, so Y

It is very common and natural in everyday Spanish. It is less formal than expressions like por lo tanto or por consiguiente.

Tuvimos que is the preterite of tener que, and here it means we had to in a specific completed situation.

That fits the sentence well:

• the doctor had no slots
• as a result, we had to postpone the appointment

It refers to one concrete necessity in the past.

By contrast, teníamos que would suggest something more ongoing, repeated, or descriptive, such as:

• When we lived there, teníamos que pedir cita con mucha antelación
  = When we lived there, we had to book appointments far in advance.

So:

• tuvimos que = one completed instance
• teníamos que = ongoing, repeated, or background necessity

No. Aplazar means to postpone, to put off, or to delay until later. It does not mean to cancel.

So:

• aplazar la cita = postpone the appointment
• cancelar la cita = cancel the appointment

A very close synonym is posponer. Both are correct:

• aplazar la cita
• posponer la cita

In Spain, aplazar sounds very natural here.

Because it refers to a specific appointment that both speaker and listener already know about.

• la cita = the appointment
• una cita = an appointment

In this sentence, it is not just any appointment. It is the appointment they had already arranged or were talking about, so the definite article is the natural choice.

Yes, Spanish often omits the subject when it is clear from context. You could say:

Ya no tenía ninguna hora disponible, así que tuvimos que aplazar la cita.

That is grammatically fine. But without context, it may be less clear who tenía refers to, so keeping El médico makes the sentence clearer.

A little, yes, but ya no usually stays together before the verb because it works as a fixed expression meaning no longer.

The most natural order is:

• El médico ya no tenía ninguna hora disponible

You may also hear things like:

• El médico no tenía ya ninguna hora disponible

That is possible, but it is less neutral and less common in this kind of sentence. For most learners, ya no tenía is the safest and most natural pattern to remember.