Answer
$(x-1)^2+(y-2)^2+(z-2)^2=4$
Work Step by Step
If $r$ is the radius and $P_0(x_0,y_0,z_0)$ is the center of the sphere, then the standard form of the equation of the sphere is:
$(x-x_0)^2+(y-y_0)^2+(z-z_0)^2=r^2.$
Hence, here:
$(x-1)^2+(y-2)^2+(z-2)^2=2^2\\
(x-1)^2+(y-2)^2+(z-2)^2=4\\$