Find the number of strings in the language $(∅∅^∗ + ∅)$
Your language could be simplified as follows, using $\emptyset^* =\{\epsilon\}$:

$$
\begin{align*}
L(\emptyset\emptyset^*+\emptyset)
&amp;=L(  \emptyset . \{\epsilon\} + \emptyset) \\
&amp;=L(\emptyset +\emptyset) &amp;    (\emptyset.\{\epsilon\}=\emptyset) \\
&amp;=L(\emptyset) &amp; (\emptyset + \emptyset = \emptyset)
\end{align*}
$$

So the language L accepts empty language which is $L =\{ \}$, which means that it contains zero elements.

Please be aware that the empty language is different from language consisting of the empty string, which is $L =\{\epsilon\}$, and which contains the element $\epsilon$, while the empty language contains zero elements.