Sie schätzt die Entfernung vorsichtig ab.

On its own, Sie can mean:

• she
• formal you
• they

But the verb form helps you narrow it down:

• sie schätzt = she estimates or formal you estimate
• sie schätzen = they estimate

Because the sentence has schätzt (singular), Sie here cannot mean they. It must mean either:

• she
• formal you

Only context tells you which one is intended.

Because the verb is abschätzen, which is a separable verb.

• infinitive: abschätzen
• in a normal main clause: schätzt ... ab

So:

• Sie schätzt die Entfernung vorsichtig ab.

This is a very common German pattern. The prefix moves to the end in main clauses:

• Ich kaufe ein. from einkaufen
• Er steht auf. from aufstehen
• Sie schätzt ab. from abschätzen

The base verb is abschätzen.

It means something like:

• to estimate
• to gauge
• to assess approximately

In this sentence, schätzt ... ab is the present-tense form of abschätzen.

schätzt is:

• 3rd person singular
• present tense
• from abschätzen

So it matches a singular subject such as:

• sie = she
• Sie = formal you

Compare:

• ich schätze ab
• du schätzt ab
• sie/Sie/er schätzt ab
• wir schätzen ab
• ihr schätzt ab
• sie/Sie schätzen ab

Entfernung is a feminine noun, so its dictionary form is:

• die Entfernung

In this sentence, it is the direct object of the verb, because it is the thing being estimated.

So grammatically it is in the accusative case. For feminine nouns, the article stays die in both nominative and accusative:

• nominative: die Entfernung
• accusative: die Entfernung

That is why the form looks unchanged.

It is accusative.

You can tell because abschätzen takes a direct object: you estimate something. Here, that something is the distance.

So the structure is:

• Sie = subject
• schätzt ... ab = verb
• die Entfernung = direct object, therefore accusative

A useful comparison with a masculine noun makes the case easier to see:

• Sie schätzt den Preis ab.

Here der Preis becomes den Preis in the accusative. With die Entfernung, nominative and accusative happen to look the same.

Vorsichtig is an adverb here. It describes how she is estimating the distance.

So it means something like:

• carefully
• cautiously

It modifies the action, not the noun. In other words:

• not the careful distance
• but she estimates it carefully

In a German main clause with a separable verb, the conjugated part of the verb comes earlier, and the prefix goes to the end. Other sentence elements can appear in between.

So the pattern is:

• subject
• conjugated verb
• other elements
• separable prefix

That gives:

• Sie schätzt die Entfernung vorsichtig ab.

This is perfectly normal.

German often places adverbs like vorsichtig in the middle part of the sentence, before the final separable prefix.

Yes, German word order is somewhat flexible, though not completely free.

For example, you could also say:

• Sie schätzt vorsichtig die Entfernung ab.

That still works, but it shifts the emphasis a bit. The original sentence:

• Sie schätzt die Entfernung vorsichtig ab.

sounds very natural and neutral.

The important fixed point is that in a main clause, the separable prefix ab normally stays at the end.

Not always.

• schätzen by itself can mean to estimate, but also to value or to appreciate
• abschätzen more specifically means to estimate/gauge/assess

So in a context like distance, size, risk, or time, abschätzen is often the clearer choice.

Examples:

• Ich schätze ihn sehr. = I appreciate/value him a lot.
• Ich schätze die Kosten. = I estimate the costs.
• Ich schätze die Kosten ab. = I assess/estimate the costs, often with the sense of making a practical estimate.

Yes. Sie schätzt ... ab is present tense.

It can mean:

• she is estimating the distance
• she estimates the distance
• formal you are estimating the distance
• formal you estimate the distance

As in English, the exact present-time meaning depends on context.

The verb stays together in some structures, especially when it is not a finite main-clause verb.

For example:

• Sie will die Entfernung vorsichtig abschätzen.
• Sie hat die Entfernung vorsichtig abgeschätzt.

But in the simple present main clause, it separates:

• Sie schätzt die Entfernung vorsichtig ab.

So a good rule is:

• main clause, conjugated verb → often separated
• infinitive or participle → usually together

A rough guide:

• sch sounds like English sh
• ä is like a short open e sound
• tz sounds like ts

So schätzt sounds roughly like shetst.

The full sentence, very roughly, is:

• Zee shetst dee ent-fair-noong for-zikh-tikh up

A few notes:

• Sie sounds like zee
• ch in vorsichtig is the soft German ich sound
• ab at the end is short and clear

Usually it refers to distance, especially physical distance, and that is the most natural meaning here.

Depending on context, it can also refer more abstractly to distance in a figurative sense, but in this sentence the most likely meaning is literal distance between two points or objects.

So die Entfernung abschätzen is a very natural phrase for:

• estimating how far away something is