Having some diffuclty

The first  isn't too difficult 

We have the form   (x - h)^2  + (y - h)^2  = r^2

The center  is ( x , h)    and the radius  =  sqrt (r^2) = r

So....we have

(x - 2)^2 + (y + 3)^2  = 80   writing this in a slightly different form we have

(x - 2)^2  + ( y - (-3) )^2  = 80

So.....the center  is   (2, -3)    and the radius  = sqrt (80)  =  sqrt (16 *5)  = 4sqrt (5)

The second one requires a little thinking

If the center of the circle lies on the line  y = 6x + 2  and the circle is tangent to the x axis  at (-2, 0)  then the the x coordinate of the center of the circle  is at  x = -2

So.....the y cordinate of the center  must be y = 6(-2) + 2  =  -10

So....the center  is  ( -2, -10)

And since this circle is tangent to the x axis......the radius must = 10

So.....the equation is   (x + 2)^2 + (y + 10)^2  = 100

See the graph here :   https://www.desmos.com/calculator/8abh7hhozi