I received your letter was dated April l6 the day before yesterday 这是一句话,一句话里面只能有一个谓语动词,而receive和be都是动词,所以有一个要成为从句或非谓语动词. 去掉BE,也就是去掉was和在前面加上that/which是一样的,就是取消was作谓语的资格,变成一个定语从句,而让receive成为整句的谓语动词
I received your letter (that was dated April l6 the day before yesterday ) 加that为定语从句,先行词是your letter。 I received your letter ( dated April l6 the day before yesterday )去was,为过去分词短语,作 your letter的后置定语