Explanation
This series is constructed by alternately multiplying the last number in the series by 1 and then subtracting 2 from the result:
2
\(2 = 2 \times 1\)
0 = 2 - 2
\(0 = 0 \times 1\)
-2 = 0 - 2
Making the next two numbers in the series:
\(-2 = -2 \times 1\)
-4 = -2 - 2