If I have these languages:
$$\begin{align*} S&=\{a,b,c,d,e,f,g,h\}\\ A&=\{b,g\}\\ B&=\{a,b,c,d,f,h\}\\ C&=\{a,c,g\}\,, \end{align*}$$
Writing $X'$ for the complement of a set $X$, what would B'∪ C consist of? Would the elements of this language then be C = {c g}?
Also if I have B ∩ (A ∪ C'), would the elements of this language then be {ab bb cb db fb hb}? Since A ∪ C' would = {b} then combined with B we have {ab bb cb db fb hb}
The union symbol $\cup$ means "everything in the first set along with everything in the second set" (ignoring duplicates).
$$ \begin{aligned} B' &= S - B &= \{e, g\}\\ B' \cup C &= \{e, g\} \cup C &= \{a, c, e, g\}\\ \end{aligned} $$
Likewise, $A \cup C'$ is (everything in $A$) together with (everything not in $C$).
$$ A \cup C' = A \cup \{b, d, e, f, h\} = \{b, d, e, f, g, h\}\\ $$
The intersection symbol $\cap$ means "only the items in both sets." It doesn't involve the creation of new elements (as in your "bb" and "cb") -- you might be thinking of Cartesian product $\times$.
So $B \cap (A \cup C')$ would be $\{b, d, f, h\}$.
Here's a Venn diagram explaining union and intersection: