。
She nearly fell off the platform.
Literal
[topic-は] almost platform [from-から] about-to-fall was.
ホーム ('platform') is a clipped loanword — short for the English 'platform,' so the loan path is platform → プラットホーム → ホーム. Native English speakers occasionally hear ホーム and parse it as 'home,' but in transit contexts it's strictly the train platform. ~そうだった is the past form of ~そうだ ('looks like'), here giving 'looked like she was about to fall.' This is parallel to the more common もう少しで...ところだった construction but more visual — emphasizing how the situation appeared in the moment. Falls from station platforms are a recurring safety concern in Japan, prompting the now-ubiquitous 'platform doors' (ホームドア) at busy stations.