(x-5)²+ (y+7)²= 16. if the circle is shifted 3 units right, and 9 units up, what is the equation of the new circle?

The coordinates of the center of this circle are (5, -7), so moving the circle 3 units right would add 3 on to the x coordinate, making it (8, -7). Then, you have to move up 9 units, adding 9 on to -7 and giving your y coordinate as 2. This makes your final coordinates (8, 2), so your equation is:
(x - 8)² + (y - 2)² = 16

I hope this helps!

(6,0) i hope it makes enough sense