Answer:
see attachment
Explanation:
The directions tell you what you need to know. It is a matter of adding up the values shown and finding the missing number to make the total be -20. Of course, it works best to start with a row, column, or diagonal that has 4 numbers already.Then, you're only finding the 5th number.
You can start with either diagonal, column 1 or 4, and row 4 or 5. Filling the missing numbers in those spots (red) will let you find the remaining missing numbers (green, then blue).
The square at row 2, column 2 can be filled on the first round using the down-right diagonal. I have shown it as filled on the second round after row 5 column 2 is filled.
Using a spreadsheet can make this easier, because you can write formulas for the sums in each row, column, and diagonal. Then you're just making those sums be -20.
___
For example, consider the up-right diagonal. The sum of the given values, -6, 0, -4, -2, is -12. Then the spot at row 1, column 5 must be filled with -8 to make the sum be -20.