No quiero ensuciar la alfombra nueva con los zapatos.

Because after querer (to want), Spanish normally uses an infinitive for the next verb:

• quiero ensuciar = I want to dirty / I want to make dirty
• literally, I want to dirty the new carpet

This is the same pattern as:

• Quiero comer = I want to eat
• No quiero salir = I don’t want to go out

So No quiero ensuciar... means I don’t want to dirty...

In Spanish, standard negation usually puts no directly before the conjugated verb:

• No quiero = I do not want

You do not normally put no before the infinitive here:

• correct: No quiero ensuciar
• not standard: Quiero no ensuciar in this everyday meaning

So the sentence is structured around I don’t want, and then the action follows.

Spanish often drops subject pronouns when the verb ending already makes the subject clear.

• quiero already tells us the subject is I
• so No quiero naturally means I don’t want

You can say Yo no quiero..., but it usually adds emphasis, contrast, or emotion:

• Yo no quiero ensuciar la alfombra nueva = I don’t want to dirty the new carpet

Without yo, the sentence sounds more neutral and natural in most contexts.

Ensuciar means to make dirty or to dirty.

It is very close to suciar, and in many contexts they overlap. Ensuciar often feels a bit like to get something dirty.

Manchar is slightly different: it often means to stain or to mark something with a spot or stain.

So:

• ensuciar la alfombra = make the carpet dirty in general
• manchar la alfombra = stain the carpet, perhaps with wine, mud, paint, etc.

In this sentence, ensuciar fits well because dirty shoes can make a carpet generally dirty.

In Spanish, adjectives often come after the noun:

• la alfombra nueva = the new carpet

That is the most neutral, ordinary order.

If you put nueva before the noun — la nueva alfombra — it is still correct, but it can sound a bit more specific or contrastive, like:

• the new carpet (as opposed to the old one)

So:

• la alfombra nueva = neutral description
• la nueva alfombra = often more emphatic or contrastive

Because la means the, so it refers to a specific carpet that both speaker and listener can identify.

• la alfombra nueva = the new carpet
• una alfombra nueva = a new carpet

If the speaker is talking about a particular carpet in the house, la makes sense.

Spanish often uses the definite article (el, la, los, las) where English would use a possessive (my, your, his, etc.), especially when the owner is obvious from context.

So:

• con los zapatos literally = with the shoes
• but in natural English here, it is often understood as with my shoes

Since the speaker is the one doing the action, it is obvious whose shoes are meant.

You can say con mis zapatos, but that adds emphasis or clarity:

• No quiero ensuciar la alfombra nueva con mis zapatos = I don’t want to dirty the new carpet with my shoes

Con means with, and here it shows the means or instrument that could cause the carpet to get dirty.

• ensuciar la alfombra con los zapatos = to dirty the carpet with shoes

It answers the idea by using what? or because of what?

Other examples:

• Corto el pan con un cuchillo = I cut the bread with a knife
• Manchó la camisa con café = He/She stained the shirt with coffee

So con los zapatos tells us what would make the carpet dirty.

Yes, that is a very natural interpretation.

Literally, con los zapatos is with the shoes, but in context it often implies:

• by stepping on it with shoes
• while wearing shoes
• because of the dirt on the shoes

Spanish does not need to spell all of that out. The context gives that meaning.

That is a different sentence.

• No quiero ensuciar la alfombra nueva con los zapatos = I don’t want to make the new carpet dirty with my shoes
• No quiero ensuciarme los zapatos = I don’t want to get my shoes dirty

The second one uses ensuciarse, the reflexive form, because the shoes themselves are becoming dirty.

So:

• ensuciar algo = dirty something
• ensuciarse = get dirty / make oneself dirty

Yes, it is possible, but the nuance changes slightly.

• ensuciar focuses on making something dirty in general
• manchar focuses more on leaving a stain or mark

If you are worried about mud, dust, or general dirt from shoes, ensuciar is often the better choice.

If you imagine a clear stain or visible marks, manchar may be more appropriate.

Yes, alfombra is a common word, but in Spain there can be a useful distinction:

• alfombra often refers to a rug
• moqueta often refers to fitted carpet / wall-to-wall carpet

In everyday speech, though, learners will often hear alfombra used broadly, and the sentence is perfectly natural.

So if you are talking about a rug on the floor, alfombra is especially good.

Yes, but the original order is the most neutral:

• No quiero ensuciar la alfombra nueva con los zapatos.

You may also hear:

• Con los zapatos no quiero ensuciar la alfombra nueva.
• La alfombra nueva no quiero ensuciarla con los zapatos.

These versions are possible, but they sound more marked, more emphatic, or more context-dependent.

For a learner, the original sentence is the best standard version to use.