1. The problem asks to find the value of $n(A \cup B)$ given $n(A) = 7$, $n(B) = 12$, and $n(A \cap B) = 6$. 2. The formula for the union of two sets is: $$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$ This formula accounts for the fact that elements in the intersection are counted twice when adding $n(A)$ and $n(B)$, so we subtract $n(A \cap B)$ once. 3. Substitute the given values into the formula: $$n(A \cup B) = 7 + 12 - 6$$ 4. Simplify the expression: $$n(A \cup B) = 19 - 6$$ 5. Calculate the final value: $$n(A \cup B) = 13$$ Therefore, the value of $n(A \cup B)$ is 13.