Progression

let $a_1$ be the first term of the arithmetic progression and $d$ be the common difference, then

$a_1=x, a_4=x+3d$ and $a_8=x+7d$

Since the above is the first three terms of a geometric progression, then

$\dfrac{a_4}{a_1}=\dfrac{a_8}{a_4}$ $\color{#D61F06}\large \implies$ $\dfrac{x+3d}{x}=\dfrac{x+7d}{x+3d}$ $\color{#D61F06}\large \implies$ $x^2+6xd+9d^2=x^2+7xd$ $\color{#D61F06}\large \implies$ $9d^2=xd$ $\color{#D61F06}\large \implies$ $x=9d$

Therefore, the common ratio of the geometric progression is,

$r=\dfrac{a_4}{a_1}=\dfrac{x+3d}{x}=\dfrac{9d+3d}{9d}\dfrac{12d}{9d}=$ $\boxed{\dfrac{4}{3}}$