Finding the equivalence classes of a language
Your language is $01^*0(0+1)^*$, i.e., all words starting with 0 and containing at least one more 0.

Indeed, a word of the form $0y0z$ is in $A$ since we can take $n=1$ and $x = y0z$. Conversely, if $w = 0^nx \in A$ then $w$ contains at least $2n \geq 2$ many 0's, and starts with a 0.

Therefore the Myhill–Nerode equivalence classes of your language are:
$$
\epsilon, 1(0+1)^*, 01^*, 01^*0(0+1)^*.
$$