Tyto krabice jsou těžké, proto je dáváme do auta opatrně.

Tyto means these.

It is the standard demonstrative form used with plural nouns like krabice. In everyday spoken Czech, many people would more often say tyhle instead of tyto.

So:

• tyto krabice = standard / neutral / a bit more formal
• tyhle krabice = very common in speech

Both mean the same thing here.

That is a very common Czech issue: some noun forms look the same in singular and plural.

Here, you know krabice is plural because of agreement in the rest of the sentence:

• tyto = plural
• jsou = plural are
• těžké = plural adjective form

So even though krabice by itself can be singular or plural in some contexts, the surrounding words make it clear that this means boxes.

Also, krabice is a feminine noun.

Because Czech adjectives must agree with the noun they describe.

The dictionary form is těžký = heavy, but the ending changes.

Here the noun is:

• krabice
• feminine
• plural
• nominative, because it is the subject

So the adjective becomes těžké.

Even though těžké comes after jsou, it still agrees with the subject. Czech does this with predicate adjectives too:

• Krabice je těžká = The box is heavy
• Krabice jsou těžké = The boxes are heavy

Proto here means therefore, so, or that is why.

It introduces the result:

• Tyto krabice jsou těžké = reason
• proto je dáváme do auta opatrně = result

By contrast, protože means because and introduces the reason itself.

Compare:

• Tyto krabice jsou těžké, proto je dáváme do auta opatrně.
  These boxes are heavy, so we put them into the car carefully.

• Protože jsou tyto krabice těžké, dáváme je do auta opatrně.
  Because these boxes are heavy, we put them into the car carefully.

So proto = result, while protože = cause.

Here je means them.

It is the accusative plural form of the third-person pronoun, referring back to krabice.

So:

• je dáváme = we put them

You are right that je can also mean is, as in:

• On je doma. = He is at home.

But that is a different word with the same spelling. Czech has several forms that look identical, and context tells you which one it is.

In this sentence, je cannot mean is, because dáváme is already the main verb.

Because je is a short unstressed pronoun, often called a clitic. In Czech, clitics usually go in the second position in the clause.

In the clause:

• proto je dáváme do auta opatrně

the first element is proto, so the clitic je comes right after it.

That is why proto je dáváme sounds natural.

A version like proto dáváme je is not the normal standard order.

This second-position behavior is very common with short forms like:

• je
• se
• si
• mi
• ti
• mu

So this sentence is also useful as a word-order example, not just a vocabulary example.

Because Czech usually does not need subject pronouns.

The verb ending already tells you who is doing the action:

• dávám = I put / I am putting
• dáváš = you put
• dáváme = we put

So dáváme already includes the idea of we.

You can add my if you want emphasis or contrast:

• My je dáváme do auta opatrně.
  We are putting them into the car carefully.

But in a neutral sentence, Czech normally leaves my out.

This is about aspect, which is very important in Czech.

• dávat = imperfective
• dát = perfective

Here, dáváme comes from dávat. It presents the action as ongoing, repeated, or simply viewed as a process.

That fits well with the idea of carefully putting heavy boxes into the car.

If you said dáme, that would usually sound like a completed, one-time action, often with future meaning:

• dáme je do auta = we will put them into the car / we’ll place them in the car

So in this sentence, dáváme is the more natural choice.

Because do means movement into something, and do requires the genitive case.

The noun is:

• dictionary form: auto
• genitive singular: auta

So:

• do auta = into the car

This is different from location:

• v autě = in the car

A useful contrast is:

• Dáváme je do auta. = We are putting them into the car.
• Jsou v autě. = They are in the car.

So do is for motion toward the inside, while v is for being inside.

Opatrně means carefully. It is an adverb, describing how the boxes are being put into the car.

It comes from the adjective opatrný = careful.

The position at the end is very natural:

• proto je dáváme do auta opatrně

Czech word order is flexible, so other placements are possible, for example:

• Opatrně je dáváme do auta.
• Proto je opatrně dáváme do auta.

But the original order sounds smooth and ordinary. Putting opatrně near the end often keeps the focus on the manner of the action.

Because there are two clauses here:

• Tyto krabice jsou těžké
• proto je dáváme do auta opatrně

The second clause is linked as a result of the first one, and Czech normally separates this kind of structure with a comma.

So the comma helps show:

• first clause = statement
• second clause = consequence

This punctuation is standard and natural in Czech.