Mohl bys mi z auta přinést ještě jednu těžkou krabici?

Mohl bys is the conditional form of moci (to be able to / can) for you in the singular informal form.

In this sentence, it works like a soft request: Could you bring... ?

Czech often uses this kind of conditional to sound less abrupt than an imperative. So:

• Přines mi... = Bring me...
• Mohl bys mi přinést... ? = Could you bring me... ?

So the sentence sounds natural, polite, and conversational rather than bossy.

Bys is a short conditional auxiliary used with ty (you, singular informal).

It comes from older by jsi, but in modern Czech bys is the normal form.

So:

• mohl bys = you could / would be able to
• udělal bys = you would do
• šel bys = you would go

It is a clitic, which means it usually stands near the beginning of the sentence, typically in second position.

Because this sentence is addressed to one male person.

In Czech, the past-participle-like part of the conditional agrees with the gender of the subject:

• Mohl bys... = said to one male
• Mohla bys... = said to one female

So if you were talking to a woman, the sentence would be:

Mohla bys mi z auta přinést ještě jednu těžkou krabici?

Mi is the dative form of já (I / me) and means to me / for me.

Here it marks the person who receives the action:

• přinést mi krabici = bring me a box

Compare:

• mě / mne = accusative (me as a direct object)
• mi / mně = dative (to me / for me)

Why the short form mi?

Because mi is the unstressed clitic form, and that is the normal choice in a sentence like this.
Mně is the longer, stressed form, used for emphasis or after prepositions.

So:

• normal: Mohl bys mi...
• emphatic: Mně bys ji přinést mohl, jemu ne.

The preposition z means from / out of, and it requires the genitive case.

The noun auto is neuter, and its genitive singular is auta.

So:

• auto = nominative
• z auta = from the car / out of the car

This is why you get z auta, not z auto.

In this sentence, z auta tells you where the box should be brought from.

Because it depends on the modal expression mohl bys.

After verbs like moci (can / be able to), Czech normally uses an infinitive:

• Můžeš přijít. = You can come.
• Mohl bys přinést... ? = Could you bring... ?

So the finite part is mohl bys, and the main action stays in the infinitive: přinést.

Přinést is the perfective verb, and that fits this situation because the speaker wants one completed action: bring one box from the car.

• přinést = to bring, as a completed act
• přinášet = to be bringing / to bring repeatedly or habitually

Since this is a single request, perfective přinést is the natural choice.

Also, the prefix při- suggests movement toward the speaker or destination, so přinést is specifically bring here / bring over rather than just carry in a general sense.

Here, ještě means another / one more / an additional.

So:

• jednu těžkou krabici = one heavy box
• ještě jednu těžkou krabici = one more heavy box

You are right that ještě can also mean still in other contexts, for example:

• Ještě spí. = He is still sleeping.

But in this sentence, because it appears with jednu, it clearly has the meaning one more.

Because krabice is a feminine singular noun, and here it is the direct object, so it is in the accusative case.

That affects the numeral and the adjective too:

• jedna → jednu
• těžká → těžkou
• krabice → krabici

So the whole phrase agrees in gender, number, and case.

A rough breakdown:

• jednu = feminine accusative singular of jeden
• těžkou = feminine accusative singular of těžký
• krabici = accusative singular of krabice

This is a very common Czech pattern: all the words modifying a noun must match it grammatically.

Yes, Czech word order is fairly flexible, but not random.

A few important points are at work here:

1. Clitics like bys and mi usually come near the beginning of the sentence.
2. The rest of the sentence can move around depending on emphasis, topic, and what sounds most natural.

This version is a natural neutral order. But other versions are also possible, for example:

• Mohl bys mi ještě jednu těžkou krabici přinést z auta?
• Mohl bys z auta přinést ještě jednu těžkou krabici pro mě?
  (grammatically possible, but less natural than mi)

The meaning stays similar, but the focus may shift slightly.
The given sentence sounds like a normal everyday request.

It is informal singular, because of bys, which goes with ty.

So you would say this to:

• a friend
• a family member
• a child
• someone you are on informal ty terms with

If you wanted the formal version to one person, you would say:

Mohl byste mi z auta přinést ještě jednu těžkou krabici?
if speaking to a man

or

Mohla byste mi z auta přinést ještě jednu těžkou krabici?
if speaking to a woman

If speaking to several people:

Mohli byste mi z auta přinést ještě jednu těžkou krabici?

Yes, but the meaning would change.

• Mohl bys mi z auta přinést těžkou krabici?
  = Could you bring me the heavy box / a heavy box from the car?

• Mohl bys mi z auta přinést jednu těžkou krabici?
  = Could you bring me one heavy box from the car?

• Mohl bys mi z auta přinést ještě jednu těžkou krabici?
  = Could you bring me one more heavy box from the car?

So ještě jednu is doing important work: it shows that this is an additional box, not just any box.

Yes: both are unstressed short forms, and Czech uses them in a very regular way.

In Mohl bys mi...:

• bys = conditional clitic
• mi = short dative pronoun clitic

These short words usually do not carry strong stress, and they like to stay near the beginning of the sentence.

That is why learners often hear Czech sentences where the meaningful content words come later, while little grammar words cluster early in the sentence.

So this sentence is a good example of a very common Czech pattern:

[first word] + [short clitics] + [rest of sentence]