Mi hija tuvo que agacharse para recoger el lápiz que se le cayó debajo de la mesa.

Both can mean had to, but they are used differently.

• tuvo que = a completed obligation in a specific situation
  
  • Mi hija tuvo que agacharse... = My daughter had to bend down... on that particular occasion.
• tenía que = a habitual, ongoing, or background obligation
  
  • De pequeña, mi hija tenía que agacharse mucho = When she was little, my daughter often had to bend down a lot.

Here, the sentence describes one completed event, so tuvo que is the natural choice.

Because agacharse means to bend down / crouch down oneself, while agachar usually means to lower something or to lower a part of the body.

Compare:

• agacharse = to crouch / bend down
• agachar la cabeza = to lower your head

In this sentence, the daughter herself bends down, so the reflexive form agacharse is used.

para + infinitive is used to express purpose: in order to or to do something.

So:

• se agachó para recoger el lápiz = she bent down to pick up the pencil

This is very common in Spanish:

• Fui al supermercado para comprar pan
• Abrió la ventana para ventilar

Yes. In this sentence, recoger means to pick up something from a surface or from the floor.

In Spain, recoger is very common for this meaning. Depending on context, it can also mean:

• to collect
• to gather
• to tidy up
• to pick someone up somewhere

Here, because of el lápiz, it clearly means pick up.

Spanish often uses the definite article (el, la, los, las) where English might use the, a, or a possessive, depending on context.

Here, el lápiz simply means the pencil. The sentence does not need to specify ownership. It is just the pencil involved in the situation.

Spanish often prefers the article when the object is already understood from context.

This part means that fell from her or, more naturally in English, that she dropped.

It is built like this:

• que = that, referring back to el lápiz
• se cayó = fell
• le = to her / from her, indicating who was affected or involved

So:

• el lápiz que se le cayó = the pencil that she dropped

Spanish often expresses this idea as something that fell on someone rather than directly saying they dropped it.

This is one of the most common questions learners have.

In se le cayó:

• cayó = fell
• se cayó = it fell
• le = to her / from her

So se le cayó literally suggests something like:

• it fell from her
• it went and fell on her

In natural English, we usually translate it as she dropped it.

This structure is very common in Spanish when something happens accidentally:

• Se me cayó el vaso = I dropped the glass
• Se te olvidaron las llaves = You forgot the keys
• Se le rompió el móvil = Her phone broke / She broke her phone depending on context

It often softens or depersonalises the action, especially with accidents.

Not exactly.

• se le cayó usually suggests something accidental
  
  • The pencil slipped from her hand / she dropped it
• dejó caer can sound more deliberate
  
  • she let it fall / she dropped it on purpose or at least more actively

So in this sentence, se le cayó is the better choice if the pencil fell accidentally.

debajo de means under / underneath.

So:

• debajo de la mesa = under the table

It is a fixed expression:

• debajo de la cama = under the bed
• debajo del sofá = under the sofa

You may also see bajo la mesa, which also means under the table, but debajo de often feels a bit more concrete or physical in everyday speech.

Because debajo normally needs de before a noun.

So:

• debajo de la mesa = correct
• debajo la mesa = incorrect

Think of debajo de as a single expression meaning under.

Here que is a relative pronoun meaning that or which.

It connects el lápiz to extra information about it:

• el lápiz = the pencil
• que se le cayó = that she dropped

So the whole phrase means:

• the pencil that she dropped

This is very common in Spanish:

• la chica que vino
• el libro que compré

Because the pronouns already make the reference clear.

In:

• Mi hija tuvo que agacharse para recoger el lápiz que se le cayó...

the le tells us the pencil fell from her, and context already tells us that her is mi hija.

Spanish often avoids repeating nouns when pronouns or context make the meaning clear.

Yes. For example:

• Mi hija tuvo que agacharse para recoger el lápiz que cayó debajo de la mesa.

This is grammatically fine, but it changes the nuance slightly.

• que cayó debajo de la mesa = that fell under the table
• que se le cayó debajo de la mesa = that she accidentally dropped under the table

The original sentence makes the daughter more clearly involved in the accident.

To some extent, yes, but the original order is the most natural.

Original:

• Mi hija tuvo que agacharse para recoger el lápiz que se le cayó debajo de la mesa.

Possible variation:

• Mi hija tuvo que agacharse para recoger el lápiz que se le cayó bajo la mesa.

But changing the order too much can sound less natural or create ambiguity. For example, Spanish prefers to keep debajo de la mesa close to the idea of where the pencil ended up.

A few useful points for Spain Spanish:

• hija: the j is a strong throaty sound
• tuvo: the v sounds like Spanish b
• recoger: the g before e sounds like the strong Spanish j
• lápiz: in most of Spain, the z sounds like th in think
• cayó: the y is a consonant-like sound, roughly like English y
• debajo: again, strong j
• mesa: in most of Spain, s is a clear s, not like Latin American aspiration in some regions

A rough pronunciation guide could be:

• Mi i-ja too-bo kay a-ga-char-se pa-ra re-ko-her el la-pith ke se le ka-yo de-ba-ho de la मे-sa

That is only approximate, but it highlights the main sounds a learner from English might notice.