Some nouns, adjectives and verbs can be followed by that-clauses. Examples are: suppose, expect, hope, say, suggest, admit, complain, tell, warn, assure, promise, inform, satisfy, confess, declare, fear, feel, intend, understand etc.

I suppose that he is not at home.

I hope that you will have a wonderful time.

It is essential that you consult a doctor.

The teacher said that he was busy.

She suggested that we should go to the park.

He confessed that he had stolen the money.

They complained that they had not been fairly treated.

That is often omitted, after verbs like say, think, suppose, hope or expect.

I think he is right. (OR I think that he is right.)

I hope you will have a great time. (OR I hope that you will have a great time.)

After some verbs, we use should + infinitive or subjunctive in the that-clause.

I insisted that she should see a doctor at once. OR I insisted that she see a doctor at once.

Some verbs are followed by an object + that-clause. Examples are: tell, warn, assure, promise, inform etc.

He told me that he was interested in the offer. (NOT He told that he was interested in the offer.)

She assured me that she would help.

I warned him that he should be careful.