Given any set $A$, the set $A\cup \emptyset=A$. (Think of starting with $A$ and then adding nothing to it). Thus, your set in question is $\\{\emptyset,\\{\emptyset\\}\\}$. This set has two elements: $\emptyset$ and $\\{\emptyset\\}$.
Given any set $A$, the set $A\cup \emptyset=A$. (Think of starting with $A$ and then adding nothing to it). Thus, your set in question is $\\{\emptyset,\\{\emptyset\\}\\}$. This set has two elements: $\emptyset$ and $\\{\emptyset\\}$.