Learn Portuguese (Portugal): A porta deste prédio é velha.

deste is a contraction of the preposition de (of) and the demonstrative este (this). In Portuguese, these two words always combine. So, deste prédio translates to of this building.

Why do we use deste here instead of desta?

Demonstratives like this have to match the gender and number of the noun they point to. Because prédio (building) is a masculine, singular noun, we use the masculine singular form este, which becomes deste when combined with de.

The word prédio is masculine, so why does the sentence end with the feminine adjective velha?

The adjective velha (old) is describing a porta (the door), which is feminine. Even though prédio is right next to the verb, the core subject of the sentence is the door, so the adjective must match it.

Why is the verb é used here instead of está?

é comes from the verb ser, which we use for permanent or long-lasting characteristics. Being old is considered a permanent trait of the door, not a temporary condition that estar would describe.