ANSWER
[tex]{(x - 4)}^{2} + {y}^{2} = 12[/tex]
EXPLANATION
The equation of a circle given the center (h,k) and radius r is given by:
[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
The circle has center (4,0) and radius
[tex]r = 2 \sqrt{3} [/tex]
We substitute the center and radius to get,
[tex]{(x - 4)}^{2} + {(y - 0)}^{2} = {(2 \sqrt{3)} }^{2} [/tex]
[tex]{(x - 4)}^{2} + {(y - 0)}^{2} = 12[/tex]
[tex]{(x - 4)}^{2} + {y}^{2} = 12[/tex]
