Emily is four years old. Her big sister Amy is three times as old as Emily. How old will Amy be when she is twice as old as Emily?

Let's start by determining the current ages of Emily and Amy.

1. Emily is currently 4 years old.
2. Amy is three times as old as Emily, so: Amy's age = 3 * Emily's age Amy's age = 3 * 4 Amy's age = 12 years old

Next, we need to find out when Amy will be twice as old as Emily. Let's assume this happens in $x$ years.

3. In $x$ years, Emily's age will be: Emily's future age = 4 + $x$

4. In $x$ years, Amy's age will be: Amy's future age = 12 + $x$

We need to find $x$ such that Amy's future age is twice Emily's future age: 12 + $x$ = 2 * (4 + $x$)

Now, solve for $x$:

5. 12 + $x$ = 2 * (4 + $x$)
6. 12 + $x$ = 8 + 2$x$
7. Subtract $x$ from both sides: 12 = 8 + $x$
8. Subtract 8 from both sides: 4 = $x$

So, $x$ = 4 years.

Finally, we determine Amy's age when this happens:

9. Amy's future age = 12 + $x$
10. Amy's future age = 12 + 4
11. Amy's future age = 16 years old

Therefore, Amy will be 16 years old when she is twice as old as Emily.