Prove that the two circles shown below are similar. circle x is shown with a center at negative 2, 8 and a radius of 6. circle y is shown with a center of 4, 2 and a radius of 3.

The picture in the attached figure

we have that
circle x
center point is (-2,8)
radius r=6 units
the equation of a circle x is
 (x+2)²+(y-8)²=6²

circle y
center point is (4,2)
radius r=3 units
the equation of a circle y is 
(x-4)²+(y-2)²=3²

we know that
If I can transform circle x to circle y using only translations, rotations and scaling  (In the case of circles, no rotations are necessary)thencircle x and circle y are similar
hence
step 1
scaling radius circle x by a factor of 0.5
r=6 units> r=6*0.5> r=3 units

step2
translate the center circle x (-2,8)
6 units at right
6 units down
(x,y)> (x+6,y-6)(-2,8)>(-2+6,8-6)> (-4,2)

now the circle x and the circle y have the same radius an the same center using only translation and scaling
therefore
circle x an circle y are similar