Try to use the circle formula!
For what value of c will the circle with equation \(x^2 + 6x + y^2 - 4y + c = 0\) have a radius of length 4?
x^2 + 6x + y^2 - 4y = -c complete the square on x and y
x^2 - 6x + 9 + y^2 - 4y + 4 = -c + 9 + 4
Note that if the radius is 4.....then the right side must = r^2 = 4^2 = 16
So
-c + 9 + 4 =16
-c + 13 =16
-c = 3
c = -3