It was handed down from my grandmother.是：它是从我婆婆那传下来的./它是婆婆传下来的.
hand down 具体上只用在
1.上代/上一辈转某样东西给下一代/下一辈/.如：祖父母从给孙子,哥传弟.
例：stories handed down from generation to generation.代代相传的故事.
Most of my clothes were handed down to me by my older brother.我的衣服大多是我哥哥传给我的.
2.正式宣布某事物/颁布某事物.如：预算,判决,裁定.
hand down from :只要说“---传----.”就可以了.