Heute brauchen wir das Wohnzimmer nicht auszuräumen; wir brauchen nur den kleinen Tisch an die Wand zu stellen.

Because German main clauses follow the verb-second rule.

That means:

• the finite verb must be in the second position
• whatever comes first can be a time word, object, adverb, etc.

So in:

Heute brauchen wir das Wohnzimmer nicht auszuräumen.

• Heute is in position 1
• brauchen is in position 2
• wir comes after that

If you started with Wir, you would get:

Wir brauchen heute das Wohnzimmer nicht auszuräumen.

That is also correct, but the emphasis is a little different.

It does mean to need, but here it is being used with an infinitive construction:

• brauchen + zu + infinitive

So:

• wir brauchen das Wohnzimmer nicht auszuräumen = we do not need to clear out the living room
• wir brauchen nur den kleinen Tisch an die Wand zu stellen = we only need to put the small table against/to the wall

In modern German, brauchen + zu + infinitive is especially common when there is a word like:

• nicht = not
• nur = only

So learners often see things like:

• Du brauchst nicht zu kommen.
• Ich brauche nur zu warten.

Because ausräumen is a separable verb, while stellen is not.

• base verb: ausräumen
• with zu: auszuräumen

In separable verbs, zu is inserted between the prefix and the base verb:

• aufmachen → aufzumachen
• einladen → einzuladen
• ausräumen → auszuräumen

But with a non-separable/simple verb like stellen, you just get:

• zu stellen

Here nicht negates the infinitive idea: not to clear out / not need to clear out.

German often places nicht before the infinitive phrase it negates, especially in structures like:

• nicht zu machen
• nicht zu sagen
• nicht auszuräumen

So:

Wir brauchen das Wohnzimmer nicht auszuräumen.

means: We do not need to clear out the living room.

If you moved nicht, the meaning or emphasis could change, and in many cases it would sound unnatural.

Because nur is focusing on what is required.

wir brauchen nur den kleinen Tisch an die Wand zu stellen

means roughly: the only thing we need to do is put the small table against the wall

Here nur limits the action to that one task. It naturally comes before the element it focuses on, or before the phrase containing that focus.

Compare:

• Wir brauchen nur den kleinen Tisch zu stellen.
  = The only thing we need to move is the small table.
• Wir brauchen den kleinen Tisch nur an die Wand zu stellen.
  = We only need to put the small table against the wall.

The exact placement can slightly shift what is being emphasized.

They are direct objects.

• das Wohnzimmer is the thing being cleared out
• den kleinen Tisch is the thing being moved/placed

So the accusative forms are:

• das Wohnzimmer → same in nominative and accusative because das does not change here
• der kleine Tisch → den kleinen Tisch in the accusative masculine

That is why you see:

• den instead of der
• kleinen instead of kleine

Because Tisch is masculine, and it is in the accusative.

The pattern is:

• nominative: der kleine Tisch
• accusative: den kleinen Tisch

Both the article and the adjective change:

• der → den
• kleine → kleinen

This is a very common pattern in German.

Because this sentence describes movement toward a destination, not a static location.

German two-way prepositions like an can take:

• accusative for direction/movement
• dative for location

So:

• den Tisch an die Wand stellen = put the table against/to the wall
  → movement, so accusative
• der Tisch steht an der Wand = the table is standing against/by the wall
  → location, so dative

That is one of the most important German preposition patterns to learn.

Because German often chooses different verbs depending on the final position of the object.

• stellen = put something so that it stands upright
• legen = lay something down flat
• setzen = set someone/something into a sitting position

A table normally stands on its legs, so:

• den Tisch an die Wand stellen

would be the natural choice.

English often just uses put, but German is more specific.

German often repeats the verb to make the structure clear and natural:

Heute brauchen wir das Wohnzimmer nicht auszuräumen; wir brauchen nur den kleinen Tisch an die Wand zu stellen.

That sounds balanced and clear:

• first: what is not necessary
• second: what is necessary

You could sometimes shorten repeated material in German, but here repeating wir brauchen is the most natural and straightforward phrasing.

ausräumen literally means something like clear out or empty out.

In this sentence, das Wohnzimmer auszuräumen suggests removing things/furniture from the living room, or at least clearing it significantly.

It is stronger than just:

• aufräumen = tidy up / clean up

So:

• aufräumen = make the room neat
• ausräumen = remove things from it / clear it out

That is why the second clause makes sense: they do not need to clear out the whole room; they only need to move one small table.

Yes. The semicolon links two closely related main clauses.

Here it shows:

• first clause: what is unnecessary
• second clause: what is necessary instead

A full stop would also be fine:

• Heute brauchen wir das Wohnzimmer nicht auszuräumen. Wir brauchen nur den kleinen Tisch an die Wand zu stellen.

A comma would usually not be correct here, because these are two independent main clauses not joined by a coordinating conjunction like und or aber.

So the semicolon is a stylistic punctuation choice that fits very well.