What is wrong with 'I do have two brothers.' ? I'm doing English grammar exercise and I think that's a correct sentence. But it isn't.
It would be helpful if you could give more information about the exercise and the context of the statement. Is it a multiple-choice or a gap-fill, for example?
Anyway, in the context of giving general information to a new acquaintance about you and your family, the sentence is ungrammatical:
I come from Thailand. I live in Bangkok. I have two brothers. I like classical music. ...
None of these simple present tense sentences are formed with the auxiliary "do". The auxiliary is only needed in negative statements and questions:
I do not have any brothers.
Do you have any brothers?
However, there are contexts in which the auxiliary "do" is indeed used in simple present statements. One such context is to contradict a statement or assumption made by your speaking partner. Assume that she does not know you very well and says:
If you had two brothers like me, you would know ... .
To contradict her assumption, you would say:
I do have two brothers,
stressing the word do. This and similar uses of an otherwise unnecessary auxiliary is often called "emphatic". There is more information here: http://www.michellehenry.fr/emphasize.htm