Use set notation to list all the elements of the set. The integers between -6 and 4 , not inclusive.

Step 1 ：We need to list all the integers between -6 and 4, but not including -6 and 4 themselves. This means we start from -5 and end at 3.

Step 2 ：Final Answer: The set of all integers between -6 and 4, not inclusive, is \(\boxed{\{-5, -4, -3, -2, -1, 0, 1, 2, 3\}}\).