Identify the part of the sentence that has an error in it.
They cannot leave the office without a special permission.

The error lies in the incorrect usage of the article 'a';
The article 'a' is not required here in the sentence.
Article 'a' and 'an' are called indefinite articles and it is used to define a noun that is unspecific whereas article 'the' is used to define a noun that is specific.
Here, in the sentence, the adjective 'special' is used to modify the noun permission and it means better, greater, or otherwise different from what is usual, therefore, it will not require an article with it.
অতএব সঠিক বাক্য: They cannot leave the office without special permission.