Working independently, Machine X can fill an order in 15 hours. Working independently, Machine Y can fill the same order in 10 hours. If Machine X works independently for 12 hours to fill an order and then Machine Y works independently to complete the order, how many hours does it take Machine Y to complete the order?

When Machine X works for 12 hours, it completes a portion of the order. Since Machine X fills the entire order in 15 hours, in 12 hours it completes \( \frac{12}{15} = \frac{4}{5} \) of the order. Therefore, there is \( 1 - \frac{4}{5} = \frac{1}{5} \) of the order remaining. Now let's see how long it takes Machine Y to fill that remaining \( \frac{1}{5} \) of the order. Since Machine Y fills the entire order in 10 hours, it can fill \( \frac{1}{10} \) of the order in 1 hour. Thus, to find out how long it takes to fill \( \frac{1}{5} \) of the order, we set up the following calculation: \[ \text{Time} = \left( \frac{1}{5} \right) \div \left( \frac{1}{10} \right) = \frac{1}{5} \times 10 = 2 \text{ hours} \] So, it takes Machine Y 2 hours to complete the order.