Given the universal set $\mu = \{x: 0 \le x \le 6\}$, and sets $A = \{0, 2, 4, 6\}$, $B = \{1, 2, 3, 4\}$, and $C = \{1, 3\}$, we want to find $A \cap (B' \cup C)$.

1. Problem Description

Given the universal set $\mu = \{x: 0 \le x \le 6\}$, and sets $A = \{0, 2, 4, 6\}$, $B = \{1, 2, 3, 4\}$, and $C = \{1, 3\}$, we want to find $A \cap (B' \cup C)$.

2. Solution Steps

First, we need to find the complement of $B$, denoted as $B'$. The universal set is $\mu = \{0, 1, 2, 3, 4, 5, 6\}$. Therefore, $B' = \mu - B = \{0, 5, 6\}$.

Next, we need to find the union of $B'$ and $C$, denoted as $B' \cup C$.

$B' \cup C = \{0, 5, 6\} \cup \{1, 3\} = \{0, 1, 3, 5, 6\}$.

Finally, we need to find the intersection of $A$ and $(B' \cup C)$, denoted as $A \cap (B' \cup C)$.

$A \cap (B' \cup C) = \{0, 2, 4, 6\} \cap \{0, 1, 3, 5, 6\} = \{0, 6\}$.

3. Final Answer

The final answer is $\{0, 6\}$.

So the correct option is B. $\{0, 6\}$.