A double fact in math is a doubled value that is easy to remember, such as the equation "8 + 8 = 16." Any doubled number is a double fact, but double facts are most commonly used when they are small numbers, usually less than 12.
The reason teachers use double facts to teach students is because they provide a faster way to find the answer to addition problems that are not as easy to memorize. For example, rather than remembering that "8 + 9 = 17," students can use double facts to come up with the answer. In this case, a student would know that the double fact of eight is 16 and that nine is one more than eight. The students then needs to add one to 16 to get the answer. The student could also remember the double fact of nine and then subtract one to get the answer.
The same technique also works for larger numbers. If a student tries to find the answer to "15 + 18," the student needs to remember that the double fact of 15 is 30. Accordingly, the student then needs to add three to that answer to get the solution.