La kuranta infano eniras la banĉambron kun malpuraj manoj.

Kuranta is the present active participle of kuri (to run).

• kuras = runs / is running
• kuranta = running

In this sentence, kuranta works like an adjective describing infano:

• la kuranta infano = the running child

So Esperanto is using a participle the same way English does in phrases like the running child or the sleeping baby.

Because it is acting as an adjective.

In Esperanto:

• nouns end in -o
• adjectives end in -a
• adverbs end in -e

Since kuranta describes the noun infano, it must take the adjective ending -a.

So:

• infano = child
• kuranta infano = running child

Because infano is the subject of the sentence, not the direct object.

The subject is the one doing the action:

• La kuranta infano = the running child
• eniras = enters

The child is the one entering, so infano stays in its basic form.

Esperanto usually adds -n to a noun when it is the direct object, not when it is the subject.

Because banĉambron is the direct object of eniras.

Here:

• eniri = to enter
• something you enter is treated as the direct object

So:

• La infano eniras la banĉambron. = The child enters the bathroom.

That is why banĉambro becomes banĉambron.

Both patterns are possible, but they are built differently.

1. eniri + direct object

• eniras la banĉambron
• literally: enters the bathroom

Here eniri is a verb meaning to enter, so the place entered becomes the direct object.

2. iri en + place

• iras en la banĉambron
• literally: goes into the bathroom

Here iri means to go, and en means into.

So the sentence uses eniri, which is often a neat, natural way to say enter.

It means with dirty hands.

• kun = with
• malpuraj = dirty
• manoj = hands

This is a prepositional phrase that describes the situation in which the child enters the bathroom. In normal understanding, it tells us something about the child:

• The running child enters the bathroom with dirty hands.

So the child has dirty hands.

Because kun is a preposition, and nouns after prepositions normally do not take -n.

So:

• kun mano = with a hand
• kun manoj = with hands

Since manoj is after kun, it stays without -n.

Also, manoj is plural because the sentence is talking about hands, not just one hand.

Because adjectives must agree with the nouns they describe.

Here the noun is manoj:

• manoj = hands, plural

So the adjective must also be plural:

• malpuraj manoj = dirty hands

Agreement in Esperanto means:

• singular noun → singular adjective
• plural noun → plural adjective
• accusative noun → accusative adjective too, if applicable

Here both are plural, so both have -j.

mal- gives the opposite meaning.

• pura = clean
• malpura = dirty

So:

• malpuraj manoj = dirty hands

This is a very common and useful Esperanto pattern:

• bona = good → malbona = bad
• granda = big → malgranda = small
• pura = clean → malpura = dirty

Because there are two separate nouns being specified:

• la kuranta infano = the running child
• la banĉambron = the bathroom

In Esperanto, just like in English, you often use the separately for each noun phrase if both are definite.

So the sentence is not saying just any child and any bathroom, but the child and the bathroom.

Yes, banĉambro literally means bath-room:

• ban- relates to bathing
• ĉambro = room

So banĉambro is a standard way to say bathroom.

Depending on context, Esperanto speakers may also use other words for related ideas, but banĉambro is very natural for bathroom.

In normal interpretation, it describes the child, not the bathroom.

So the meaning is:

• The running child enters the bathroom, and the child has dirty hands.

Grammatically, the phrase is attached to the whole action, but semantically it most naturally refers to the child. A bathroom does not normally have hands, so the meaning is clear from context.

Yes, Esperanto has fairly flexible word order, although some orders sound more natural than others.

For example, these are still understandable:

• La infano kuranta eniras la banĉambron kun malpuraj manoj.
• Kun malpuraj manoj la kuranta infano eniras la banĉambron.

However, the original:

• La kuranta infano eniras la banĉambron kun malpuraj manoj.

is clear and natural.

Esperanto word order is flexible because endings like -n and -j carry a lot of the grammatical information, but learners should usually start with straightforward, natural orders like the one in this sentence.