应该说:suggest (that) sb. do sth. (美国英语) / suggest (that) sb. should do sth.(英国英语)/ suggest someone's doing sth. 例如:
I suggested he should adapt himself to his new conditions. 我建议他适应新的环境。
Tom suggested my selling the house . 汤姆建议我把房子卖掉。
(以上例句摘自赵振才编著的《英语常见问题解答大词典》增订版第1380页)
He suggests that she get a job in a bank. 他建议她在银行里找份工作。
He suggested that she get a job in a bank. 他曾建议她在银行里找份工作。
(以上例句《牛津英语用法指南》第三版570.3节)
2. advise that sb. do sth. / advise sb. to do sth. / advise someone's doing st. 例如:
I advised that he go at once. 我劝他马上去。
The doctor advised Father to cut down on smoking. 医生劝父亲少抽烟。
I advised his starting at once .我劝他马上出发。
(以上例句《薄冰英语惯用法词典》第31页)
3. 以下用法也正确,但是目前在其它书刊中极少看到,所以在考试中最好不用:
Her uncle suggests that she gets a job in a bank . 他叔叔建议她在银行里找份工作。
He suggested that she got a job in a bank. 他曾建议她在银行里找份工作。