She is having an affair with her Japanese teacher on the sly.

她和她的日文老师偷偷有了恋情。

He's been drinking whiskey on the sly for thirty years.

他暗中偷喝威士忌酒已有三十年了。

When she thought no one was looking she opened the cupboard and took a few sweets on the sly.

当她觉得没人看见时，她打开壁橱偷偷拿了几块糖。