1. The problem asks to find the result of the set operation $A \cup (A \cap B)$ where $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$.\n\n2. First, find the intersection $A \cap B$, which is the set of elements common to both $A$ and $B$.\n$$A \cap B = \{3, 4\}$$\n\n3. Next, find the union of $A$ with the intersection $A \cap B$. The union $A \cup (A \cap B)$ includes all elements in $A$ or in $A \cap B$. Since $A \cap B$ is a subset of $A$, the union is just $A$.\n$$A \cup (A \cap B) = A = \{1, 2, 3, 4\}$$\n\n4. Therefore, the answer is $\{1, 2, 3, 4\}$, which corresponds to option c.