(x- h)^2+(y- k)^2= r^2
In this form, ( h, k) is the center of the circle and r is its radius. We are told that the center of the circle is the origin, which is the point ( 0, 0) and its radius is 4. This information is enough to write the equation.
(x- 0)^2+(y- 0)^2= 4^2
⇕
x^2+y^2=16