> for what value of c will the circle with equation > x^2+6x+y^2-4y+c=0 have a radius of 4

Hint: Rewrite the above equation in the form (x-x0)^2 + (y-y0)^2 = r^2 and set the r^2 you obtain (depending on c) to 4^2. Then solve for c. The result will be c=-3.