The line with equation $y=-2x+c$ 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 $c=\boxed{{\displaystyle \frac{561}{68}}}$