Después del viaje, tuve que deshacer la maleta enseguida.

Because de + el contracts to del in Spanish.

• después de el viaje → incorrect
• después del viaje → correct

This contraction happens almost always with de + el.
A similar example is:

• al viaje = a + el viaje

One important exception: there is no contraction if el is part of a proper name, such as de El Escorial.

Tuve que is the preterite of tener que, which means to have to / had to.

• tener que + infinitive = to have to do something
• tuve que deshacer = I had to unpack

The preterite is used because this refers to a completed event in the past: after the trip, at that moment, the speaker had the obligation to unpack.

Compare:

• Tuve que deshacer la maleta. = I had to unpack the suitcase.
  (specific completed situation)
• Tenía que deshacer la maleta. = I had to / was supposed to unpack the suitcase.
  (background situation, ongoing obligation, or less focus on completion)

Yes. Deshacer is built from:

• hacer = to do / to make
• des- = a prefix meaning undo / un-

So deshacer literally means something like to undo. In this context, deshacer la maleta means to unpack.

It is a very common Spanish expression. Spanish often says undo the suitcase where English says unpack the suitcase.

You may also hear:

• hacer la maleta = to pack
• deshacer la maleta = to unpack

In Spanish, the definite article is used more often than in English.

So:

• deshacer la maleta = unpack the suitcase / unpack one’s suitcase

Even if English might say unpack my suitcase or simply unpack, Spanish very naturally uses la maleta when the object is understood from context.

Other possibilities are also possible depending on emphasis:

• deshacer mi maleta = unpack my suitcase
  (more explicit, more personal emphasis)
• deshacer la maleta = unpack the suitcase / my suitcase
  (natural when it is obvious whose suitcase it is)

Yes, but it changes the structure slightly.

• Después del viaje = after the trip
• Después de viajar = after travelling / after traveling

Both are grammatical, but después del viaje sounds more like a specific trip seen as a noun event, while después de viajar focuses more on the action of travelling itself.

In your sentence, después del viaje is very natural because it refers to a specific trip that has just ended.

Enseguida means right away, immediately, or straight away.

So:

• deshacer la maleta enseguida = unpack the suitcase right away

It suggests very little delay.

Similar words:

• inmediatamente = immediately
  (more formal)
• al momento = right away
• en cuanto llegué = as soon as I arrived
  (different structure, but often used in similar contexts)

In Spain, enseguida is very common in everyday speech.

No, it does not have to be at the end. Spanish adverbs often have flexible placement.

Your sentence has:

• Después del viaje, tuve que deshacer la maleta enseguida.

But you could also say:

• Después del viaje, enseguida tuve que deshacer la maleta.
• Después del viaje, tuve que enseguida deshacer la maleta.
  This one is much less natural.

The most natural positions are usually:

• at the end
• before the main verbal idea for emphasis

So in this sentence, the final position sounds very natural.

Because tener needs que before another verb when it means to have to.

The structure is:

• tener que + infinitive

Examples:

• Tengo que salir. = I have to leave.
• Tuve que estudiar. = I had to study.
• Tendré que llamar. = I will have to call.

Without que, the sentence is incorrect in this meaning.

Yes. Deshacer follows the irregular pattern of hacer.

Some useful forms:

• hacer → hago, hice, hecho
• deshacer → deshago, deshice, deshecho

Examples:

• Deshago la maleta. = I unpack the suitcase.
• Deshice la maleta. = I unpacked the suitcase.
• He deshecho la maleta. = I have unpacked the suitcase.

In your sentence, deshacer appears in the infinitive because it comes after tuve que.

The preterite of tener is irregular. Its stem changes to tuv-.

Here is the full preterite:

• tuve
• tuviste
• tuvo
• tuvimos
• tuvisteis
• tuvieron

So:

• tuve que = I had to
• tuviste que = you had to
• tuvo que = he/she had to

This is a very important irregular verb to learn because it is extremely common.

Not usually in the same way.

• maleta = suitcase
• equipaje = luggage / baggage

Deshacer la maleta is the normal expression for unpack the suitcase.

You would not normally say:

• deshacer el equipaje in the same everyday way

It can be understood, but it is less idiomatic in many contexts. For a learner, hacer/deshacer la maleta is the safest and most natural expression.

The comma separates the introductory time phrase from the main clause:

• Después del viaje, = after the trip,
• tuve que deshacer la maleta enseguida. = I had to unpack the suitcase right away.

In English, a comma after an introductory phrase is also common. In Spanish, this comma is natural and helps readability, though in short sentences punctuation can sometimes vary.

Yes. The sentence would still be correct:

• Tuve que deshacer la maleta enseguida.

That means I had to unpack the suitcase right away.

Adding después del viaje gives the time context and makes the sentence more specific:

• After the trip, I had to unpack the suitcase right away.

So the first part is optional in grammar terms, but it adds useful information.

In Spain, a typical pronunciation would include these features:

• c before e/i is pronounced like the th in think
• z is also pronounced like th
• v and b sound very similar in Spanish
• h is silent

So roughly:

• Después → des-PWES
• viaje → bee-AH-he or bya-he
• tuve → TOO-beh
• que → keh
• deshacer → de-sah-THER in Spain
• maleta → mah-LEH-tah
• enseguida → en-seh-GHEE-dah

That is only an approximation using English spelling, but it highlights the main Spain-specific point: deshacer has the th sound in Peninsular Spanish.

Yes, it is completely natural.

It sounds like normal everyday Spanish, especially because of expressions like:

• después del viaje
• tener que + infinitive
• deshacer la maleta
• enseguida

A native speaker from Spain would understand it immediately and would likely use very similar wording.