Please help me out on this sentences and please explain if there is any rule concerning these types of statements

"In the forthcoming elections every man and woman must vote for the candidate of their choice"

Great question.

There would seem to be three options:

(1) Use his and explain at the start of the document (if appropriate) that his means his/her.

(2) Use his/her (or his or her), but this is clumsy.

(3) Use their, but this is might appear grammatically unsound due to the change in number from singular to plural. (It is, however, an accepted convention.)

The choice is yours. All three are correct. Yes, even the last one (despite what some might tell you).

Thank you! :)

We've added a page on his/her and their.

"their" is NOT correct grammar. The pronoun must fit the singular subject.