suggest them doA.I suggest they start the work right now.B.I

是A
动词suggest有如下一些用法:
一、 有"建议"的意思.advise,propose 也有此义,请比较它们用法的异同:
1) 都可接名词作宾语
She suggested / advised / proposed an early start.她建议早一点出发.
We suggested / advised / proposed a visit to the museum the next day.我们建议明天去参观博物馆.
2) 都可接动名词作宾语
I suggested / advised / proposed putting off the sports meet.我建议将运动会延期.
They suggested / advised / proposed waiting until the proper time.他们建议(我们)等到恰当的时机才行动.
3) 都可接that 宾语从句,that从句用should+动词原形,should可以省略.
She suggested / advised / proposed that the class meeting (should) not be held on Saturday.她建议班会不要在星期六举行.
We suggested / advised / proposed that he (should) go and make an apology to his teacher.我们建议他去向老师道歉.
4) advise 可接动词不定式复合宾语,propose 可接不定式作宾语.
I advised him to give up the foolish idea.= I suggested / proposed his / him giving up the foolish idea.我建议他放弃那愚蠢的念头.(suggest和propose在口语里可接动名词的复合宾语).
We proposed to start early.= We proposed starting early.我们建议早一点出发.(接不定式不用suggest和advise)
二、 有"提出"的意思.如:
He suggested a different plan to his boss.他向老板提出了一个不同的计划.
Xiao Wang suggested a way to solve the problem.小王提出了一个解决这个问题的办法.
三、 有"暗示、表明"的意思.其主语往往是事物,而不是人.
1)接名词或动名词作宾语.
The simple house suggested a modest income.这座简朴的房子表明(房主的)收入并不高.
Her pale face suggested bad health.她脸色苍白,看来身体不好.
The thought of summer suggests swimming.一想到夏天就使人们联想到游泳.
2)接宾语从句,从句用陈述语气.如:
The decision suggested that he might bring his family.这个决定表明他可以把家属带来.
The expression on his face suggested that he was very angry.他脸上的表情表明他很生气.
四、 在主语从句It is suggested that...及名词suggestion 后面表示具体建议的表语从句、同位语从句都应用should+动词原形,should可以省略.如:
It was suggested that we (should) give a performance at the party.人们建议我们在晚会上表演节目.
His suggestion was that the debts (should) be paid off first.他的建议是先把债务还清.
The doctors made a suggestion that the new hospital (should) not be set up on the hill.医生们建议不要把新医院建在山上

正确的是suggest that sb. should do， 用虚拟语气，should可以省略，所以是A。
没有suggest sb do sth这个句型。
suggest的另外一个句型是suggest doing sth