Learn Italian: Ma noi cerchiamo una nuova casa con un terrazzo grande. - But we are looking for a new house with a large terrace.

Placing nuova before the noun means it is new to the speaker, meaning they just want to move to a different house. If we placed the adjective after the noun (una casa nuova), it would specifically mean a brand-new, recently built house.

Why does grande come after terrazzo?

When grande is placed after the noun, it describes literal physical size, so this means the terrace is spacious. If it were placed before the noun (un grande terrazzo), it would mean a great or impressive terrace.

Why isn't there a word for "for" after cerchiamo?

The verb cercare already means "to look for" or "to search for" all on its own. You do not need to add a preposition like per to say what you are looking for.

Do we have to include noi in this sentence?

It is not strictly required because the -iamo ending on cerchiamo already tells us the subject is "we". Adding noi here just gives a little extra emphasis, as if saying "But we are looking for..."