Learn Hardcore Catalan: Aquesta part és fàcil.

Aquesta is the feminine singular form of this in Catalan. It has to agree with the noun it modifies. Since part is a feminine singular noun, you use aquesta part.

The basic forms are:

aquest = this (masculine singular)
aquesta = this (feminine singular)
aquests = these (masculine plural)
aquestes = these (feminine plural)

So:

aquest llibre = this book
aquesta part = this part

Is part really feminine? It doesn’t end in -a.

Yes. In Catalan, grammatical gender is not always obvious from the ending. While many feminine nouns do end in -a, plenty do not. Part is a feminine noun, so it takes feminine words with it:

aquesta part
la part
una part

This is something you often just have to learn with the noun.

Why is there no article before part?