#### Answer

$(A' \cup C) \cap B'=\color{blue}{\left\{6, 7, 8\right\}}$

#### Work Step by Step

$A'$ is the set that contains the element/s of the universal set $U$ that are not elements of $A$.
Thus,
$A' = \left\{7, 8\right\}$
$A' \cup C$ is the set that contains the combined elements of $A'$ nd $C$.
Thus,
$A'\cup C=\left\{1, 6, 7, 8\right\}$
$B'$ is the set that contains the elements of the universal set $U$ that are not elements of $B$.
Thus,
$B' = \left\{2, 4, 6, 7, 8\right\}$
$(A' \cup C) \cap B'$ is the set the contains elements that are common to both $(A' \cup C)$ and $B'$.
Note that the elements common to both sets are: 6, 7, 8
Therefore,
$(A' \cup C) \cap B'=\color{blue}{\left\{6, 7, 8\right\}}$