Li montras la pojnon kaj la genuon.

Because they are the direct objects of montras.

In Esperanto, the thing directly affected by the verb usually takes the accusative ending -n. Here, the person is showing the wrist and the knee, so both nouns get -n:

• pojno → pojnon
• genuo → genuon

The word kaj does not change anything about the case, so both nouns stay in the accusative.

Each ending has its own job:

• -o = noun
• -n = accusative, usually for a direct object

So genuon breaks down like this:

• genu- = the root
• -o = noun
• -n = direct object

The same pattern appears all the time in Esperanto. It is very regular.

-as is the present-tense verb ending.

Esperanto verbs always use fixed endings:

• -as = present
• -is = past
• -os = future
• -us = conditional
• -u = command or wish
• -i = infinitive

So montras means shows or is showing, depending on context.

Esperanto often uses la with body parts when the possessor is obvious from the situation.

So if it is clear whose body is being indicated, la pojnon kaj la genuon can sound perfectly natural. This is similar to how Esperanto often says things like Li levis la manon for He raised his hand.

If you want to make it explicit that they are his own body parts, you can say:

Li montras sian pojnon kaj sian genuon.

Here sian is the reflexive possessive, used when the possessor is the subject of the sentence.

Repeating la is very normal and very clear:

la pojnon kaj la genuon

It makes it obvious that both nouns are definite.

A single la can sometimes cover both nouns in a pair, but repeating it is often the clearest choice, especially in simple teaching sentences like this one.

Yes. Esperanto word order is fairly flexible because the -n ending shows which words are the objects.

The most neutral order is:

Li montras la pojnon kaj la genuon.

But you could also say:

La pojnon kaj la genuon li montras.

That version puts more emphasis on the body parts. Even so, the original sentence is the most straightforward and natural for a beginner.

A helpful approximation is:

• pojnon = POY-non
• genuon = geh-NU-on

A few pronunciation points:

• j sounds like English y
• oj sounds like the vowel in boy
• stress in Esperanto falls on the second-to-last syllable

So:

• pojno = POY-no
• pojnon = POY-non
• genuo = geh-NU-o
• genuon = geh-NU-on

It can cover several close meanings, depending on context:

• show
• indicate
• point out
• sometimes almost point to

In a sentence about body parts, montras often suggests that he is indicating those parts, perhaps by gesture. So the exact English wording can vary a little, even though the Esperanto verb stays the same.