Let's look at the pattern of changes:
-6 - 3 = -9
12 - -6 = 18
4 - 12 = -8
20 - 4 = 16
The changes have a pattern of -9, -8, continuing to -7, -6, and so on, and a pattern of 18, 16, continuing to 14, 12, and so on.
The sequence -9, 18, -8, 16, should continue like this: -9, 18, -8, 16, -7, 14, -6, 12, and so on.
After the 16 would be -7, so 20-7=13
The next number should be 13.
Note: This isn't the only solution. There are an infinite number of solutions, but this should be the simplest solution. It should be the one your teacher/book is looking for.