How many ordered pairs of sets \((A, B)\) have the properties:

1. \( A \subseteq \{1, 2, 3, 4, 5, 6\} \)
2. \( B \subseteq \{2, 3, 4, 5, 6, 7, 8\} \)
3. \( A \cap B \) has exactly \(3\) elements.

Let's think step by step and output the final answer within \boxed{}.
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