at the instance of

1. 经……的提议
   I did it at the instance of one of my colleagues.

   我是经我一位同事的提议才做了这件事。

for instance

1. 例如
   You can't depend on her: for instance, she arrived late yesterday.

   她靠不住，举例说，昨天她就来迟了。

in the first instance

1. 首先
   In the first instance we had better make sure the calculations are correct.

   首先我们最好保证计算是正确的。

• at first instance
  Law  at the first court hearing concerning a case.
• at the instance of
  formal at the request or instigation of.
• for instance
  as an example.
• in the first (or second etc.) instance
  in the first (or second etc.) stage of a proceeding.