Learn Polish: Dach naszego domu jest czerwony. - The roof of our house is red.

In Polish, showing possession or translating the word of requires the Genitive case. Since we are talking about the roof of our house, both the adjective nasz (our) and the noun dom (house) change to their Genitive forms: naszego domu.

I thought masculine nouns usually end in -a in the Genitive. Why does dom change to domu?

Masculine inanimate nouns (things and concepts) can take either -a or -u in the Genitive singular. There is no perfect rule for this, so you have to learn the ending with the word. Dom is one of the common words that takes the -u ending.

Can I change the word order to say naszego domu dach, like our house's roof?

It is much better to put the possessor after the object being possessed. Dach naszego domu sounds completely natural, while putting the Genitive part first sounds overly poetic or awkward.

Why does the adjective czerwony end in -y?

Adjectives must match the noun they describe. Here, czerwony describes the subject of the sentence, dach (roof), which is a masculine singular noun in the Nominative case. Therefore, it takes the standard masculine ending -y.