Mi forĵetas malnovan paperon en la rubujon post la leciono.

Because paperon is the direct object of the verb forĵetas.

In Esperanto, the thing directly affected by the action usually gets the accusative ending -n:

• Mi legas libron = I read a book
• Mi forĵetas paperon = I throw away a paper / piece of paper

Here, the thing being thrown away is paperon, so it takes -n.

Because adjectives in Esperanto agree with the nouns they describe.

So if the noun is:

• singular: the adjective is singular too
• plural: the adjective is plural too
• accusative: the adjective also takes -n

That gives:

• malnova papero = an old paper
• malnovan paperon = an old paper (as the direct object)
• malnovaj paperoj = old papers
• malnovajn paperojn = old papers (as direct objects)

So malnovan matches paperon.

Because en can mean either:

• in/inside a place, with no movement: en la rubujo
• into a place, with movement toward it: en la rubujon

In this sentence, the paper is being thrown into the trash can, so Esperanto shows that direction with -n:

• La papero estas en la rubujo = The paper is in the trash can
• Mi metas la paperon en la rubujon = I put the paper into the trash can

This is a very common pattern in Esperanto.

forĵetas comes from:

• ĵeti = to throw
• for- = away, off
• -as = present tense

So forĵeti means to throw away.

This kind of prefix is very common in Esperanto. The prefix for- adds the idea of removal or distance:

• foriri = to go away
• forpreni = to take away
• forĵeti = to throw away

So Mi forĵetas... means I throw away...

No. In forĵetas, for- is a prefix, not a separate word.

So the normal form is:

• forĵeti
• forĵetas
• forĵetis
• forĵetos

Not ĵetas for.

Esperanto often builds words this way: a root plus a prefix gives a new, very transparent meaning.

rubujo is built from:

• rubo = trash, rubbish
• -uj- = container or holder
• -o = noun ending

So rubujo literally means something like trash-container.

That is why it means trash can, bin, or wastebasket.

This word-building system is one of the most useful parts of Esperanto.

Because la means the, and Esperanto uses it only when something is definite.

In this sentence:

• malnovan paperon = an old paper / some old paper
  
  • no la, so it is not being presented as a specific one already identified
• la rubujon = the trash can
  
  • probably a specific trash can known from the situation
• la leciono = the lesson
  
  • probably a specific lesson already understood from context

If you wanted to mean the old paper, you could say:

• la malnovan paperon

It can depend on context.

papero can refer to:

• paper as a material
• a piece/sheet of paper
• sometimes a paper/document

In this sentence, because it is singular and something being physically thrown away, it will usually be understood as a piece of paper or a paper item.

If you want to be more specific, Esperanto can do that too, for example:

• folio de papero = a sheet of paper

But papero is normal here.

Because post already expresses the relationship after.

Here, la leciono is simply the reference point in time:

• post la leciono = after the lesson

There is no direct object role here, and no motion being shown, so no extra -n is needed.

Compare:

• post la leciono = after the lesson
• la sekvan tagon = the next day

In the second example, Esperanto uses the accusative directly for time expressions without a preposition. But after post, the normal form here is post la leciono.

Yes. Esperanto word order is fairly flexible because endings show what each word is doing.

The basic order here is:

• Mi = subject
• forĵetas = verb
• malnovan paperon = direct object
• en la rubujon = direction
• post la leciono = time

But you could also say:

• Post la leciono mi forĵetas malnovan paperon en la rubujon.
• Malnovan paperon mi forĵetas en la rubujon post la leciono.

These are still understandable because -n marks the object and the directional phrase.

Still, the original order is very natural and straightforward.

It can mean either, depending on context.

The ending -as is the present tense, but Esperanto simple present is broader than English simple present. It can mean:

• something happening now
• something that regularly happens
• a general present statement

So Mi forĵetas malnovan paperon... could mean:

• I am throwing away an old paper...
• I throw away an old paper...

If you really want to emphasize an ongoing action, Esperanto can do that with a more explicit form, but the simple -as form is very common and natural.

You would make both the noun and adjective plural, and keep the accusative:

• Mi forĵetas malnovajn paperojn en la rubujon post la leciono.

Breakdown:

• malnovaj = old (plural)
• paperoj = papers
• malnovajn paperojn = old papers as the direct object

So the pattern is:

• plural: -j
• accusative: -n
• both together: -jn