How many solutions are there to the system of equations $y=-2 x^{2}+2$ and $y=-6$ ? (Enter DNE if the answer doesn't exist.)

Step 1 ：The system of equations is given by \(y=-2 x^{2}+2\) and \(y=-6\).

Step 2 ：To find the number of solutions, we need to find the number of x-values for which both equations are true.

Step 3 ：This means we need to set the two equations equal to each other and solve for x.

Step 4 ：Setting \(-2 x^{2}+2 = -6\), we find two solutions for x, which are -2 and 2.

Step 5 ：Therefore, there are two points where the two equations intersect.

Step 6 ：Final Answer: \(\boxed{2}\).