In a game, you can win different amounts of money based on the roll of a fair 6-sided die. If you roll a 1, you win $2. If you roll a 2, you win $4. If you roll a 3, you win $6. If you roll a 4, you win $8. If you roll a 5, you win $10. If you roll a 6, you win $12. Calculate the expected value of the amount of money you will win. Let's think step by step and output the final answer within \boxed{}.
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