Apartigu la metalon de la vitro.

Apartigu is the -u form, which is used for commands, requests, instructions, or exhortations in Esperanto.

So:

• apartas = is separate / are separate
• apartigi = to separate or more literally to make separate
• apartigu = separate!

In this sentence, Apartigu la metalon de la vitro. means Separate the metal from the glass.

The -ig- ending is a very common Esperanto element meaning to cause or to make something become a certain way.

Here is the idea:

• aparta = separate, distinct
• apartiĝi = to become separated
• apartigi = to separate something, to make it separate

So apartigu is literally something like make [it] separate.

This is very typical Esperanto word-building, and it is useful to recognize it because you will see -ig- in many verbs.

The -n ending marks the direct object.

In this sentence:

• la metalon = the thing being separated
• de la vitro = from the glass

So metalon gets -n because it is the direct object of apartigu.

Vitro does not take -n here because it is part of the prepositional phrase de la vitro. The preposition de already shows its role, so no accusative is needed.

Here de means from.

So:

• la metalon = the metal
• de la vitro = from the glass

In many contexts, de can also mean of, but in this sentence it clearly has the sense of separating one thing from another.

La is the definite article, meaning the.

So:

• la metalon = the metal
• la vitro = the glass

Esperanto has only one definite article: la. It does not change for gender, number, or case.

It appears before both nouns because both are definite in the sentence.

Usually vitro means glass as a material, not a drinking glass.

So:

• vitro = glass, the substance/material
• glaso = a glass, drinking vessel

Because the sentence says Apartigu la metalon de la vitro, it most naturally means Separate the metal from the glass material.

If you wanted to say from the drinking glass, you would more likely use de la glaso.

Yes, Esperanto word order is fairly flexible, because endings show grammatical function.

For example, these would still be understandable:

• Apartigu de la vitro la metalon.
• La metalon apartigu de la vitro.

But Apartigu la metalon de la vitro. is the most straightforward and natural order for a simple instruction.

The -u form can be used for many tones, depending on context:

• a direct command
• an instruction
• a request
• a polite directive

So Apartigu la metalon de la vitro. could sound like:

• Separate the metal from the glass.
• Please separate the metal from the glass.
• You should separate the metal from the glass.

The exact tone depends on the situation, not just the grammar.

Because that would mean something different.

• Apartigu la metalon de la vitro. = separate the metal from the glass
• Apartigu la metalon kaj la vitron. = separate the metal and the glass

The version with de clearly shows that one thing is being separated from the other. Without de, the meaning changes.

The dictionary forms are:

• metalo = metal
• vitro = glass

Then the sentence uses:

• metalon = metalo
  • -n because it is the direct object
• vitro = unchanged, because it follows the preposition de

This is a very common pattern in Esperanto: learn the base noun in -o, then recognize case endings when they are added.