I had to think of a way of preventing him from following me around all morning.

这句话意思是我必须要想一个办法来阻止他一个早上都跟着我。
prevent Sb. form doing sth.意思是阻止某人做某事
例：Pull the line taut to prevent it form knotting up.
把线拉紧，以免打结。

prevent form是词组，固定搭配

prevent somebody from doing something
是固定搭配。防止某人做某事

prevent from sth. 固定搭配

防止什么什么

我需要想个办法防止他以早晨都缠着我

我要想个办法防止他整个早上都缠着我。

I had to think of a way of preventing him from following me around all morning.
prevent接from在英语中是个固定搭配；
prevent sb. from doing sth. 阻止某人做某事。
相关用法还有：
prohibit sb. from doing sth.
stop sb. from doing sth.
keep sh. from doing sth.