There was a suggestion by the teachers that the meeting should bepostponed for a week.

问题一：句中的 by the teachers 实为 put forward by the teachers 之省略，所以可翻译为“由老师们提出的”。句意为：老师们建议会议延迟一周。

介词 by 的类似用法：

It’s a play by Shakespeare. 那是莎士比亚写的剧本。（= It’s a play written by Shakespeare.）

He has a painting by Hockney. 他收藏有霍克内的一幅画儿。（= He has a painting painted by Hockney）

The next selection is by Mozart. 下面的乐章选自莫扎特的作品。（= The next selection is composed by Mozart.）

问题二：表命令、建议等含义的动词之后的宾语从句通常用“should+动词原形”这样的虚拟语气；类似地，表示命令、建议的名词后若跟同位语从句，从句也通常要用“should+动词原形”这样的虚拟语气。如：

Soon came the order that all the people should obey the rules. 不久命令下来了，所有的人不得违犯制度。

There was a suggestion thatBrown should be dropped from the team. 有一项建议是布朗应该离队。

问题三：句中的 that 从句是同位语从句，用以说明 suggestion 的具体内容。