My brother is 4 times as old as I am. Six years from now, he will be twice as old as I will be.  How old is my brother now?
Suppose I am $y$ years old now.  My brother is 4 times as old as I am, so my brother's age is $4y$. Six years from now, my brother will be $4y+6$ years old and I will be $y+6$ years old. Since my brother will be twice as old as I am at that time, we must have \[4y+6 = 2(y+6).\]Expanding the right side gives $4y + 6 = 2y + 12$. Subtracting $2y$ from both sides gives $2y + 6 = 12$, and subtracting 6 from both sides gives $2y = 6$.  Dividing both sides by 2 gives $y = 3$.  The question asks for the age of my brother now, which is $4y = \boxed{12}$.  (Always make sure you answer the question.)