Quiero encargar una tarta de chocolate para el cumpleaños de mi hija.

Quiero encargar means I want to order. It expresses your intention.

• Quiero encargar una tarta... = I want to order a cake...
• Encargo una tarta... = I order / am ordering a cake...

So quiero + infinitive is a very common structure for saying want to do something.

In Spain, encargar often means to place an order for something that will be prepared for you, especially in a shop or bakery.

• encargar una tarta = order a cake in advance
• pedir una tarta = order/request a cake, but this can sound more general
• comprar una tarta = buy a cake

So encargar is especially natural if you are arranging for the cake to be made or reserved.

Because Spanish usually drops subject pronouns when they are not needed.

• Quiero already tells us the subject is I
• Yo quiero is also correct, but the yo is usually only added for emphasis, contrast, or clarity

So the sentence sounds natural without yo.

In Spain, tarta is the most natural word for a cake like a birthday cake or chocolate cake.

• tarta = cake, especially a whole decorated or dessert-style cake
• pastel in Spain often means pastry or can be used in other contexts, but it is not always the default word for a birthday cake

So for Spain Spanish, una tarta de chocolate is the most natural choice.

Spanish often uses de + noun where English uses a noun as an adjective.

• tarta de chocolate = chocolate cake
• helado de vainilla = vanilla ice cream
• zumo de naranja = orange juice

So de chocolate literally means of chocolate, but in natural English we translate it as chocolate.

Because para expresses purpose or intended recipient/use.

Here, the cake is intended for the birthday.

• para el cumpleaños de mi hija = for my daughter’s birthday

Por would not sound natural here. In this sentence, para is the correct preposition.

Spanish often uses the definite article where English does not.

• para el cumpleaños de mi hija
• literally: for the birthday of my daughter
• natural English: for my daughter’s birthday

The article el is normal here because it refers to a specific birthday event.

Mi hija means my daughter, which matches the speaker in quiero (I want).

• mi = my
• su = his / her / your / their

If you said su hija, it could be ambiguous, because su can refer to several different people. Mi hija is clear and direct.

Because cumpleaños is a noun, and Spanish possession is often expressed with de.

• el cumpleaños de mi hija = my daughter’s birthday
• literally: the birthday of my daughter

Spanish does not normally form possession the same way English does with ’s. Instead, it commonly uses de.

The personal a is used before a direct object that is a person.

Example:

• Veo a mi hija = I see my daughter

But in your sentence, mi hija is not a direct object of the verb. It is part of a de phrase:

• el cumpleaños de mi hija

So there is no personal a here.

This is a very common pattern:

querer + infinitive

• quiero comer = I want to eat
• quiero salir = I want to go out
• quiero encargar = I want to order

The first verb (quiero) is conjugated, and the second verb (encargar) stays in the infinitive.

Yes, both can sound more polite than Quiero encargar..., especially in a shop.

• Quiero encargar una tarta... = direct, natural
• Quisiera encargar una tarta... = more polite/formal
• Me gustaría encargar una tarta... = I would like to order a cake

In Spain, all three are possible, but quisiera and me gustaría are often softer and more courteous.

Yes. Cumpleaños is one of those words that looks plural but can be singular.

• el cumpleaños = the birthday
• los cumpleaños = the birthdays

So in your sentence, el cumpleaños de mi hija is singular: my daughter’s birthday.

Yes, but the original order is the most neutral and natural.

Standard order:

• Quiero encargar una tarta de chocolate para el cumpleaños de mi hija.

You could move parts around for emphasis, but it may sound less neutral:

• Para el cumpleaños de mi hija, quiero encargar una tarta de chocolate.

That version is also correct, but it puts extra focus on for my daughter’s birthday.

A helpful approximate pronunciation is:

coom-pleh-AH-nyos

A few points:

• ñ sounds like ny in canyon
• the stress is on -a-: cumpleAÑos
• cumpleaños is one word

So: cum-ple-A-nyos, with the stress on the second-to-last syllable.

Yes, but it would mean something slightly different.

• para el cumpleaños de mi hija = for my daughter’s birthday
• para mi hija = for my daughter

The original sentence focuses on the occasion.
If you say para mi hija, the focus is on who the cake is for.

You could even combine both:

• Quiero encargar una tarta de chocolate para mi hija por su cumpleaños.

But the original version is very natural and specific.