Different Intersection I

Fix $0 \leq a,b \leq n$. Let $A$ and $B$ be subsets of $[n]$ that are independently and uniformly at random selected from the collection of subsets of sizes $a$ and $b$, respectively. Find $\mathbb{E}\left[ |A\cap B| \right]$ when $a = 6, b = 8,$ and $n = 12$.