Ne marche pas sur le parquet avec tes chaussures mouillées, tu risques de l’abîmer.

Because this is a negative command in the tu form.

• Tu marches = you walk / you are walking
• Ne marche pas ! = Don’t walk!

In affirmative tu commands, French usually drops the final -s of -er verbs:

• Marche ! = Walk!

To make it negative, French puts ne ... pas around the verb:

• Ne marche pas ! = Don’t walk!

So Ne marche pas is the imperative, not a normal statement.

Because in the tu imperative of regular -er verbs, the final -s is usually dropped.

Compare:

• Tu marches = normal present tense
• Marche ! = command

This happens with many common verbs:

• Tu regardes → Regarde !
• Tu fermes → Ferme !
• Tu écoutes → Écoute !

So Ne marche pas is the correct tu command form.

Sur means on or onto, and le parquet means a wood floor or hardwood flooring.

So marcher sur le parquet means to walk on the wooden floor.

A useful detail:

• parquet usually refers specifically to a finished wooden floor indoors.
• It is more specific than sol, which just means floor/ground in a general sense.

French often uses a possessive adjective where English might leave it out.

So French says:

• avec tes chaussures mouillées
  literally: with your wet shoes

Even though English often just says with wet shoes, French naturally prefers your shoes here because they are the listener’s shoes.

This is very common in French:

• Lève la main = Raise your hand
• Ferme les yeux = Close your eyes
• Mets ton manteau = Put on your coat

Because mouillées agrees with chaussures, which is:

• feminine
• plural

The adjective must match the noun:

• un soulier mouillé = masculine singular
• une chaussure mouillée = feminine singular
• des souliers mouillés = masculine plural
• des chaussures mouillées = feminine plural

Since chaussures is feminine plural, the correct form is mouillées.

Yes. The comma separates the warning/command from the reason or consequence.

The sentence works like this:

• Ne marche pas sur le parquet avec tes chaussures mouillées = don’t do this
• tu risques de l’abîmer = because you might damage it

This kind of structure is very natural in spoken and written French:

• Ne touche pas à ça, tu vas le casser.
• Dépêche-toi, tu vas être en retard.

It is a straightforward way to give an instruction and then explain the risk.

Risquer de + infinitive means to risk doing something or, more naturally in English, to be likely to do something bad or unwanted.

So:

• tu risques de l’abîmer = you risk damaging it
• very natural English: you might damage it

Other examples:

• Tu risques de tomber. = You might fall.
• On risque d’être en retard. = We might be late.

It often suggests a possible negative consequence.

L’ stands for le, meaning it.

It refers back to le parquet.

So:

• abîmer le parquet = to damage the wooden floor
• l’abîmer = to damage it

Because parquet is masculine singular, the direct object pronoun is le, which becomes l’ before a vowel:

• le parquet → l’abîmer

Abîmer means to damage, to spoil, or to wear out something without necessarily completely breaking it.

That makes it a good choice for a floor, because wet shoes may harm it, stain it, or ruin the finish, but not literally break it.

Compare:

• abîmer = damage, spoil
• casser = break
• salir = make dirty

So here abîmer is the most natural verb.

The circumflex accent (î) is part of the spelling of the word: abîmer.

For many learners, the main thing to know is:

• you must write it
• it does not dramatically change the basic pronunciation for most modern speakers

So just learn the spelling as a whole:

• abîmer = to damage

Its noun is:

• un abîme = an abyss but that is a different word and meaning.

Yes. This sentence is addressed to one person informally.

Clues:

• Ne marche pas = tu command
• tes chaussures = your shoes for tu

If you wanted to speak formally to one person, or to use vous, you would say:

• Ne marchez pas sur le parquet avec vos chaussures mouillées, vous risquez de l’abîmer.

So the original sentence is natural when speaking to:

• a child
• a friend
• a family member
• someone you address with tu

In spoken informal French, many speakers do drop ne:

• Marche pas sur le parquet...

However, in standard written French and in careful speech, ne is normally kept:

• Ne marche pas sur le parquet...

So:

• Ne marche pas... = standard, correct, neutral
• Marche pas... = very common in conversation, but more informal

It mainly tells you in what condition / with what the person is walking, so it goes with marche:

• Ne marche pas sur le parquet
• avec tes chaussures mouillées

In other words: Don’t walk on the wooden floor while wearing your wet shoes.

French often uses avec this way to describe what someone has on or is carrying:

• Ne viens pas avec tes bottes sales.
• Il est entré avec son manteau trempé.

So here it means something like with your wet shoes on.