Cuando vio tantas cajas, mi madre se echó a reír y dijo que la mudanza parecía larguísima.

Vio is the preterite of ver. It presents the seeing as a completed event: she saw the boxes at that moment.

If you used veía, it would sound more like an ongoing background scene, such as when she was seeing / while she could see them, which is not the idea here.

So:

• Cuando vio tantas cajas... = When she saw so many boxes...
• Cuando veía tantas cajas... would suggest a repeated or ongoing situation, which is less natural here.

The subject is mi madre.

Spanish often omits subject pronouns because the verb forms already give enough information, and the noun can appear later in the sentence. Here, the sentence starts with a time clause:

• Cuando vio tantas cajas = When she saw so many boxes
• then we get mi madre = my mother

So all three verbs refer to the same person:

• vio = my mother saw
• se echó a reír = my mother burst out laughing / started laughing
• dijo = my mother said

This is very normal in Spanish word order.

Echarse a + infinitive is a common structure meaning to suddenly begin doing something.

So:

• se echó a reír = she started laughing
• often more naturally in English: she burst out laughing

It gives a stronger, more sudden feeling than simply rió (she laughed).

Here, se is part of the fixed pronominal expression echarse a + infinitive.

It is not really reflexive in the literal English sense of herself. You should learn echarse a reír as a chunk meaning:

• to start laughing
• to burst out laughing

Similar expressions include:

• echarse a llorar = to start crying
• echarse a correr = to start running

Que introduces reported speech or what someone said/thought.

So:

• dijo que la mudanza parecía larguísima = she said that the move seemed very long / endless

This is the normal pattern:

• dijo que... = said that...
• pensó que... = thought that...
• creía que... = believed that...

Also, it should be dijo que, not dijo de que. Adding de would be a common mistake called dequeísmo.

Parecía is the imperfect, which often describes an impression, state, or background view rather than a single completed action.

Here, the idea is that, from her perspective, the move seemed extremely long. That feeling is presented as an ongoing impression at that moment.

Compare:

• parecía larguísima = it seemed incredibly long
• pareció larguísima = it seemed incredibly long at that moment with more of a completed-event feel

Both can be possible in some contexts, but parecía sounds more natural here because it describes how the move looked/appeared to her.

Larguísima comes from larga plus the suffix -ísima.

• larga = long
• larguísima = very, very long / extremely long

This suffix is called an absolute superlative and is very common in Spanish.

Examples:

• grande → grandísimo = huge / extremely big
• claro → clarísimo = very clear
• largo → larguísimo = extremely long

Because mudanza is feminine singular, the adjective is also feminine singular:

• la mudanza parecía larguísima

Both are possible, but they are not exactly the same.

• muchas cajas = many boxes
• tantas cajas = so many boxes

Tantas adds a sense of emphasis or reaction. It suggests the number was striking or surprising.

Also, tantas agrees with cajas:

• feminine plural noun: cajas
• feminine plural determiner: tantas

In Spain, mudanza commonly means a house move / moving house / the move.

So in this sentence, la mudanza refers to the whole moving process, not just one physical act of transporting something.

Depending on context, English might translate it as:

• the move
• moving house
• the removal (less common in everyday modern English)

Spanish word order is flexible. Starting with Cuando vio tantas cajas puts the time/event first, a bit like setting the scene:

• When she saw so many boxes, my mother...

Then the main clause introduces the subject:

• mi madre se echó a reír...

This is completely natural Spanish. You could also say:

• Mi madre, cuando vio tantas cajas, se echó a reír...

But the original version is smoother and more typical for storytelling.

Yes, very important.

• echó has an accent because it is the 3rd person singular preterite of echar: he/she threw / started.
• Without the accent, echo is a different word, such as I throw or the noun echo, depending on context.

And:

• parecía needs the accent to show the correct stress and vowel sequence.
• It is pronounced with a clear break: pa-re-CÍ-a.

Accent marks in Spanish are not optional; they can change both pronunciation and meaning.

Yes, it can.

Cuando with the preterite in a narrative often means:

• when
• once
• as soon as

The exact English translation depends on the tone and context. In this sentence, because her reaction is immediate, English could naturally say:

• When she saw so many boxes...
• As soon as she saw so many boxes...

Both work.

Yes, grammatically it could, but the nuance changes.

• rió = she laughed
• se echó a reír = she started laughing / burst out laughing

The original is more vivid and expressive. It suggests an immediate reaction on seeing the boxes. So se echó a reír is a better storytelling choice here.