Answer
the distance between the spheres is
$2\sqrt 3$ $-$ $($ $2+1$ $)$ $=$ $2\sqrt 3$ $-$ $3$
Work Step by Step
The first sphere, $x^{2}$ $+$ $y^{2}$ $+$ $z^{2}$ $=$ $4$
the center is $($ $0$, $0$, $0$, $)$ , radius is $2$
The second sphere, $x^{2}$ $+$ $y^{2}$ $+$ $z^{2}$ $=$ $4x$ $+$ $4y$ $+$ $4z$ $-$ $11$
we can rewrite this equation to
$(x-2)^{2}$ $+$ $(y-2)^{2}$ $+$ $(z-2)^{2}$ $=$ $1$
center is $($ $2$, $2$, $2$ $)$ , radius is $1$
So, the distance between the center is $\sqrt{(2-0)^{2}+(2-0)^{2}+(2-0)^{2}}$ $=$ $2\sqrt 3$
the distance between the spheres is
$2\sqrt 3$ $-$ $($ $2+1$ $)$ $=$ $2\sqrt 3$ $-$ $3$
