Debajo del capó, mi madre encontró un cable suelto.

Because del is the mandatory contraction of de + el in Spanish.

• debajo de = under / underneath
• el capó = the bonnet/hood

So:

• debajo de el capó → incorrect
• debajo del capó → correct

This contraction happens with de + el almost always.
Compare:

• al = a + el
• del = de + el

Debajo de means under / underneath / below.

In this sentence:

• Debajo del capó = Under the bonnet/hood

You can often use bajo in a similar way:

• Bajo el capó, mi madre encontró un cable suelto.

That is also correct, but debajo de often feels a bit more literal and physical, like something being underneath something else.

A useful distinction:

• debajo de = underneath, beneath
• bajo = under, below, sometimes also more abstract

Examples:

• El gato está debajo de la mesa. = The cat is under the table.
• Trabaja bajo presión. = He/She works under pressure.

For this sentence, debajo del capó sounds very natural.

The phrase Debajo del capó has been moved to the front of the sentence for emphasis or style.

Normal order could be:

• Mi madre encontró un cable suelto debajo del capó.

When Spanish puts this location phrase first, a comma is often used:

• Debajo del capó, mi madre encontró un cable suelto.

It works a bit like English:

• Under the hood, my mother found a loose cable.

The comma is not changing the basic meaning; it just marks that fronted introductory phrase.

Encontró is the preterite form of encontrar and refers to a completed action in the past:

• mi madre encontró = my mother found

This suggests a specific event: she found it at a particular moment.

Encontraba is the imperfect, which would usually suggest:

• repeated action
• ongoing background action
• a less bounded situation

So:

• Mi madre encontró un cable suelto. = She found a loose cable.
  (a completed event)

Compare:

• Mi madre encontraba cables sueltos a menudo. = My mother used to find loose cables often.

In your sentence, the preterite is the natural choice.

Not in this form. Encontró is a regular -ar verb in the preterite.

Conjugation of encontrar in the preterite:

• yo encontré
• tú encontraste
• él/ella encontró
• nosotros encontramos
• vosotros encontrasteis
• ellos encontraron

One thing to notice is the written accent:

• encontró = he/she/it found
• encontro = not a correct standard form here

The accent helps show the stress and also distinguishes the tense/person.

In Spanish from Spain, capó means the bonnet of a car. In American English, that is the hood.

So:

• debajo del capó = under the bonnet / hood

This is a good example of regional vocabulary. In Spain, capó is standard for a car’s hood/bonnet.

Also, note the accent:

• capó

It is stressed on the last syllable: ca-PÓ.

Because in Spanish, adjectives usually come after the noun.

• un cable = a cable
• suelto = loose

So:

• un cable suelto = a loose cable

This is the normal, neutral word order.

Putting an adjective before the noun is possible in some cases, but it often changes the tone, style, or meaning. For a physical description like loose, the standard order is definitely:

• cable suelto

Here, suelto means loose, not properly attached, or detached.

So un cable suelto is:

• a loose cable
• a cable that has come free
• a cable that is not fixed in place

Suelto can have other meanings in different contexts, for example:

• dinero suelto = loose change
• un perro suelto = a dog running loose
• estar suelto = to be loose / free / not tied down

In this sentence, the mechanical meaning is the important one.

Mi madre is a neutral and very common way to say my mother.

Spanish has several options, and they differ in tone:

• mi madre = my mother (neutral/standard)
• mi mamá = my mum / my mom (warmer, more informal)
• madre by itself is less likely in this kind of sentence unless the context already makes it clear

So this sentence is simply using a standard, neutral expression.

In Spain, mi madre is very natural.

Because un cable suelto is a thing, not a specific person.

The personal a is usually used before specific human direct objects:

• Vi a mi madre. = I saw my mother.
• Encontré a Juan. = I found Juan.

But with objects or things, Spanish normally does not use that a:

• Encontró un cable suelto. = She found a loose cable.

So the absence of a is exactly what we expect here.

Yes, absolutely. That is probably the most neutral word order.

• Mi madre encontró un cable suelto debajo del capó.

This version puts the location at the end, which is very common in Spanish.

The original sentence:

• Debajo del capó, mi madre encontró un cable suelto.

brings the location to the front, giving it a little more focus. Both are correct.

It is often taught as an adverb, but in practice you will frequently see it in the structure debajo de + noun.

For learners, the most useful thing is to remember the pattern:

• debajo de la mesa
• debajo del capó
• debajo de la cama

So even if grammar books classify it in a more technical way, the important point is that when a noun follows, you normally use:

• debajo de

Not just debajo by itself.

It is pronounced with the stress on the last syllable:

• ca-PÓ

The written accent tells you that the stress falls there.

That final ó is important. Without the accent, a learner might wrongly try to stress it differently.

A simple pronunciation guide for English speakers could be:

• kah-POH

with the stress clearly on POH.

Yes, in everyday use it often refers generally to the area under the car’s hood/bonnet, not necessarily literally underneath the metal panel itself.

So if someone says:

• Debajo del capó, mi madre encontró un cable suelto.

the natural interpretation is that she found a loose cable in the engine compartment, under the hood.

This is similar to English, where under the hood can mean the whole space inside that part of the car.