Learn Hardcore Japanese: tika no kyuukou hoomu ha totemo sizuka datta. - The express platform in the basement was very quiet.

の here links two nouns in a genitive/attributive relationship. It connects 地下 (“underground” or “subway”) to 急行ホーム (“express platform”), indicating that the platform belongs to or is part of the subway. So 地下の急行ホーム literally means “the subway’s express platform.”

Why is ホーム written in katakana?

ホーム is a loanword (gairaigo) from English home, but in Japanese it means “train platform.” Loanwords are conventionally written in katakana to show their foreign origin.

Why is は used instead of が after ホーム?

は marks the topic of a sentence (“as for the platform…”), whereas が marks the subject, often used to introduce new information or emphasize it. Here, you’re simply setting 地下の急行ホーム as the topic to comment on its quietness, so は is the natural choice.

What type of adjective is 静か, and why do we need だった?

静か is a な-adjective, not an い-adjective. In predicate position, な-adjectives require the copula だ/です (or its past form だった/でした) instead of conjugating directly. So the past plain form is 静かだった (“was quiet”).

Why isn’t there a な between 静か and だった?

When a な-adjective is used predicatively (to make a statement), you drop the な and attach the copula. The な only appears when the adjective directly modifies a noun (e.g., 静かな場所).

What role does とても play, and why does it come before 静かだった?

とても is an adverb meaning “very.” Adverbs in Japanese precede the words they modify, so とても comes before 静かだった to intensify “was quiet” into “was very quiet.”

How would you express this sentence in polite/formal Japanese?

Replace the plain past copula だった with the polite past でした, giving:
地下の急行ホームはとても静かでした。