Analysis: Based on the statement "after moving 2 apples from the first pile to the second pile," we can write an algebraic expression for the first pile as $a-2$. Let's assume the second pile originally had $b$ apples. Then, according to "the number of apples in the second pile is exactly twice the number of apples in the first pile," we can derive an equation $2(a-2) = b + 2$. Solving for $b$ will give us the answer.

Let's solve the equation $2(a-2) = b + 2$:

$$\begin{align*} 2(a-2) &= b + 2 \\ 2a - 4 &= b + 2 \\ 2a - 6 &= b \end{align*}$$

Therefore, the second pile originally had $\boxed{2a - 6}$ apples.