The line with equation $y=-2 x+c$ is tangent to the curve with equation $y=-x^{2}+4$. The value of $c$ is

Step 1 ：Rearrange the equation of the line: $y = -2x + c$ to get $-2x = y - c$

Step 2 ：Substitute this into the equation of the curve: $y = -x^2 + 4$ to get $y = -(-2x)^2 + 4$

Step 3 ：Now we have $y = -4x^2 + 4$, and we can substitute $y - c$ for $-2x$

Step 4 ：So, $y - c = -4(-2x)^2 + 4$, which simplifies to $y - c = -16x^2 + 4$

Step 5 ：Now we have $y = 16x^2 + c$, and we can substitute this into the equation of the curve: $y = -x^2 + 4$

Step 6 ：So, $16x^2 + c = -x^2 + 4$, which simplifies to $17x^2 + c - 4 = 0$

Step 7 ：Since we have a tangent, this quadratic will have a double root, so its discriminant will be 0

Step 8 ：Hence, $(-17)^2 - 4(17)(c - 4) = 289 - 68c + 272 = 0$

Step 9 ：This simplifies to $561 - 68c = 0$, which means $c = \boxed{\frac{561}{68}}$