Because it would be dangerous to have fragile things falling from a high place during an earthquake, I keep plates and things inside a cupboard that is not tall.
ご質問ありがとうございます。
"Because it would be dangerous to have fragile things falling from a high place"＝「壊れものが高い所から落ちるのは危ないので」
"during an earthquake,"＝「地震のときに」
"I keep plates and things inside a cupboard that is not tall."＝「お皿などを背の低い食器棚に入れています。」
ご参考に。
アメリカ合衆国 
