可以省略.不能省略的情况为：
宾语从句不省略that的几种情况
1.当that作learn,answer,suggest,explain,agree,wonder,prove,mean,state,feel,hold等动词的宾语时;
He answered that he was from Austria.他说他是奥地利人.
She answered that she preferred to eat alone.她回答说她愿意独自吃.
I don’t wish to imply that you are wrong.我无意暗示你错了.
The newspapers have implied that they are having an affair.报纸报道暗指他们有染.
2.当宾语从句较长时;
The dealer told me how much he was prepared to pay for my car and that f could have the money without delay.
那个商人告诉我他准备出多少钱买我的汽车,并说我会立即收到款.
3.宾语从句位于句首时.
That our team will win,I believe.我相信我们队会赢.
4.当主语谓语动词(包括非谓语动词)与宾语从句之间有插入语时;
Little Alice didn't know,I'msure,that her sister was going to America.我确信,小艾丽斯不知道她的姐姐很快就要去美国了.
We hope,on the contrary,that he will stay at home with us.恰恰相反,我们希望他和我们呆在家里.
5.当一个动词带有两个或两个以上宾语从句时,此时第一个that可以省略,第二个以及其他的that不可以省略;
I hope (that) I can get a good mark and that I can go to collage
He said (that) the book was very interesting and that(不省略) all the children like to read it.
The teacher told the students (that) they should hand in their homework the next day and that the homework must be signed names by their parents.
老师告诉学生他们要在第二天交上作业,并且作业必须由家长签名.
6.当宾语从句中的主语是this,that或this,that做主语的定语时;
7.当宾语从句有双宾语中的间接宾语时;
He told me that he was leaving for Japan.他告诉我他要去日本
当that 宾语从句是双宾语中的直接宾语时,that一般不宜省略.例如：
I will never tell anyone that you have ever been there.我绝对不会告诉别人你曾经去过那儿.
8.当宾语从句的主语是非谓语动词或主语从句时;
9.当主语中的谓语动词是固定词组时;
Mary has made up her mind that she will study hard for the scholarship,so she can have the chance to go abroad for further study.
玛丽下定决心努力学习以获得奖学金资格,这样她就有机会出国深造了.
10.当宾语从句有it做其先行词时;即 it作形式宾语时.
I think it necessary that he should stay here.我们认为他有必要留在这里.
11.在直接引语中,转述分句把宾语从句隔开时.或that从句单独回答问题时.
—What did he hear?他听说了什么事?
—That Kate had passed the exam.(他听说)凯特考试及格
12.在except等介词后.如：
He has no special fault except that he smokes too much.他除了抽烟太多之外,没有什么特别的毛病.
14.在较为正式或不常用的动词（如reply,object）后.如：
He replied that he disagreed.他回答说他不同意.
15.当主句的状语部分位于that 宾语从句之前时,that不宜省略.例如：
Jane realized at once that she must do with it herself.
珍立刻意识到她必须亲自处理那件事.(如省略that,at once也可能修饰从句,是表示“立刻意识到……”,还是表示“立刻去处理……”,较为含糊)
16.Tom promised that if he could earn as much as 500 dollars in this month,he would buy a computer for his brother.
汤姆许下诺言,如果他在这个月里能够赚到500美元,他就给他的弟弟买台电脑.