Learn Turkish: Küflenmiş duvarlara ve yıpranmış halılara dikkat etmelisin. - You must pay attention to the moldy walls and worn-out carpets.

This is the past participle being used as an adjective, which is the focus of this lesson. The verb küflenmek means to get moldy, so küflenmiş describes something that has already gotten moldy. Similarly, yıpranmak means to get worn out, making yıpranmış mean worn out. It describes a current state that resulted from a completed past action.

Why do both duvar (wall) and halı (carpet) have the -a ending here?

The verb dikkat etmek (to pay attention / to be careful) always requires the dative case for the object you are focusing on. Since you are paying attention to the walls and carpets, you add the dative suffix to get duvarlara and halılara.

If the nouns are in the dative case (duvarlara), why don't the adjectives (küflenmiş, yıpranmış) take the same ending?

In Turkish, adjectives never take plural or case suffixes when they describe a noun. Even though some languages require adjectives to match the noun's case, in Turkish you only add the plural -lar and dative -a to the noun itself.

What makes up the word etmelisin at the end?