We can set Maggie's age to x
If her brother is six years younger than four times her age, than her brother must be equal to: 4x-6
Since the sum of their ages is 39, we can set up an equation.
(Sum of Maggie's age) + (sum of Maggie's brother's age) = 39
x + (4x -6) = 39
5x -6 = 39
5x = 45
x = 9 , Maggie's age is 9